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What is a compound interest calculator and how to use it in 2022 in the Philippines

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Compound interest calculators are mostly used to calculate compound interest on an investment, 401K, or savings account with annual, quarterly, daily, or continuous compounding.

The calculator can answer your compound interest queries and show the steps to calculate the final interest. Users can also experiment with the calculator to see how different interest rates or loan terms can affect how much they will pay in compound interest on a loan.

Compound interest is the interest you earn on both your initial money and the added interest (more money), which allows your savings to grow faster over time. At the end of every compound interest period, based on your savings and the returns you make, it is then added to the original principal amount, and as your corpus gets larger, you earn more returns, resulting in higher yields.

For instance, if you put ₱100,000 in savings account with a 0.50% annual yield compounded daily, you would earn ₱510 in the first and second years and ₱530 in the third year. So a total of ₱5,130 in interest would have accrued over 10 years.

When you invest in the stock market, you do not earn on a set interest rate, but rather a return calculated based on the change in the value of your investment. When you start getting higher interest rates, you earn better returns. If you leave your money and the returns you earn in the market, those returns are compounded over time in the same way interest is compounded.

For instance, if you put ₱1,000,000 initial investment into a mutual fund and it gave you a 7% return for the year, you would gain about ₱70,000, and your investment would be ₱1,070,000. If you received an average 7% return the following year, your investment would be worth about ₱1,001,500. Over the years, your investment can grow tremendously. For example, if you put ₱1,000,000 in a retirement account for 30 years and an annual interest rate raised, averaging 7% return, ₱1,000,000 would turn into more than ₱7,612,255.04 after the investment tenure is complete.

In reality, returns on investment will vary from year to year and even day to day; riskier investments, such as stocks or stock mutual funds, may lose value in the short term. But over a long time horizon, history has shown that a diversified growth portfolio can yield an average of 6% to 7% per year. Investment returns are typically reported as an annual rate of return.

The stock market's average annual percentage yield was 10% in the past, but inflation has slashed this rate, and investors can expect inflation to lower their purchasing power by 2% to 3% a year. If you are willing to wait years or decades before letting compounding work its magic, you can realize far more than what you started with. However, if you want to calculate all this in advance, you can use the compound interest calculator to calculate the earned interest you will receive.

A compound interest calculator is a financial instrument and a computerized tool that allows you to calculate the compounded interest without spending too much time or doing long calculations. It already has a compound interest rate formula box filled out in the online tool. You must enter the initial balance of principal, interest rate, time periods, etc. on the tool according to your needs. The calculator is a free tool that calculates the interest and the future value on loans or savings and the compounding rates. You can calculate the compound interest on an initial principal (initial balance) on a daily, monthly, or yearly basis.

This tool has a formula box in which you must enter the principal, the annual nominal interest rate, and time in days, months, or years. The calculator will display the interest added on the loan or the investment and the future value. The tool is simple to use; to calculate compound interest, you need to enter the following information:

The principal amount

The annual nominal interest rate

The time in decimal years

After entering this data, press the **Calculate **button; the compound interest calculator will use the compound interest formula to determine the compound interest in seconds. You will then get the same interest you receive or pay during the term.

The calculator uses the compound interest formula to calculate principal plus interest through the compound interest table. The same formula calculates principal, interest, or time when the other known values are given. You can know how compound interest grows by using this formula to set up a compound interest calculator.

The formula is **A = P(1 + r/n)^nt**;

Where:

A = Accrued amount (principal + interest) or initial investment

P = Principal amount

r = Annual nominal interest compounding rate when it is given as a decimal

R = Annual nominal interest compounding rate when it is given as a percent

r = R/100

n = number of compound periods which is a per unit of time

t = time in decimal years; For example, 9 months is calculated as 0.75 years. To get the decimal years, divide your partial year number of months by 12.

The basic compound interest formula A = P(1 + r/n)^nt can be used to find any other variables apart from the compound interest. Below is the compound interest formula which has been rewritten so that the unknown variables are isolated on the left side of all the equations.

To calculate accrued amount i.e., principal + interest; A = P(1 + r/n)^nt

To calculate the principal amount, it will solve for P in terms of A; P = A / (1 + r/n)^nt

To calculate the principal amount, it will solve for P in terms of I; P = I / [(1 + r/n)^nt - 1]

To calculate the rate of interest as a decimal; r = n((A/P)^1/nt - 1)

To calculate the interest compounding rate in percent; R = r x 100

To calculate the time, it will solve for t; t = ln(A/P) / n[ln(1 + r/n)], then also

t = [ln(A) - ln(P)] / n[ln(1 + r/n)] (*Note that ln is the natural logarithm)

For continuous compounding(n → ∞), the formulas are:

To calculate the accrued amount i.e., principal + interest; A = Pe^rt

To calculate the principal amount, it will solve for P in terms of A; P = A / e^rt

To calculate the principal amount, it will solve for P in terms of I; P = I / (e^rt - 1)

To calculate the rate of interest when it is given as a decimal; r = ln(A/P) / t (*Note that ln is the natural logarithm)

To calculate the rate of interest when it is given as a percent; R = r * 100

To calculate the time, it will solve for t; t = ln(A/P) / r (*Note that ln is the natural logarithm)

Interest is compounded either at the start or the end of the compounding period in savings accounts and investments. If additional regular deposits or withdrawals are included in your calculation, you can incorporate them either at the beginning or the end of each compounding period.

The power of compound interest becomes particularly apparent when you look at a long-term growth chart, such as the one below, which shows an initial balance of ₱10,000 investments. Because we want to keep the investment simple, we will use a longer compounding investment period (20 years) at a 10% effective annual rate. Comparing the benefits of compound interest against common interest and no interest makes it clear how compound interest can increase your investment value.

For example, compound interest of 10% for 20 years on a ₱10,000 investment will become:

0 year = ₱10,000

2 years = ₱12,203.91

4 years = ₱14,893.54

6 years = ₱18,175.94

8 years = ₱22,181.76

10 years = ₱27,070.41

12 years = ₱33,036.49

14 years = ₱40,317.43

16 years = ₱49,203.03

18 years = ₱60,046.93

20 years = ₱73,280.74

The online calculator instantly shows you the amount you will have to pay or receive after the maturity period, i.e., the future value of the investment. The following are examples of investments where the interest can be compounded for growth using the compound interest calculator:

Savings accounts

Money market accounts

Dividend stocks

Cryptocurrency investing

Roth IRA

401(k)

ISA (UK)

The following are the lines of credit that charge compound interest:

Mortgage

Home equity loans

Auto loan

Student loan

A personal loan from a financial institution or credit union

Small business loan

Credit card accounts

There are two compound interest calculators: the periodic compounding calculator and the continuous compounding calculator. Some online compound interest calculations are made specifically for either of these two, and some are made for both.

Under this calculator, the interest rate is applied only at intervals and generated. This interest is then added to the principal. Periods here mean annually, bi-annually, monthly, or weekly.

There are two formulas the calculator can use to calculate compound interest, depending on what result you wish to find out.

The total value of the deposit.

The total compound interest earned.

Formulas can be a deterrent for many if you aren't familiar with math; your eyes turn away from them or don't bother with them at all. It isn't complicated at first, but once you know how it works, the formula to determine the value of your deposit is as follows:

P (1+ i/n)^nt

Where;

P = Principal balance.

i = The nominal rate of interest.

n = Compounding frequency or number of compounding periods each year; it could also be called the snowball effect frequency.

t = Time, which means the length of time the interest is applicable, generally in years.

For instance, if your bank generates compound interest quarterly, there will be four quarters in a year, so n = 4. This sum must be multiplied by the deposit period to gain significant power. For instance, if your deposit is for 10 years, t = 10. This combined result should be multiplied by the initial principal you deposited so that the total accumulated value of your deposit is calculated. After accumulating interest, you can find out how much your deposit is worth today.

To find out the total interest earned, the calculator can use the formula for compound Interest: **P[(1+ i/n)^nt -1]**.

Instead of calculating interest on a finite number of occasions, such as yearly or monthly, a continuous compounding calculator computes interest on an infinite number of occasions by assuming constant compounding.

The continuous compounding formula is:

A = Pe^rt

Where;

P = the initial amount

A = the final amount

r = the rate of interest

t = time

e is a mathematical constant, which is ≈ 2.7183.

**Example 1**: Someone is investing money, let's say ₱300,000, in a bank that pays an annual interest rate of 7% compounded continuously. What amount can the person get after 5 years from the bank?

First of all, input the given data in the calculator, thus;

The initial amount or present value, P = ₱300,000.

The interest rate, r = 7% = 7/100 = 0.07.

Time, t = 5 years.

The calculator will now use the formula A = Pe^rt

i.e. A = 300000 × e^0.07(5) ≈ 425,720.26

Therefore the tool calculates this, and the amount the person will get after 5 years is ₱425,720.26.

**Example 2**: If someone borrowed money, let's say ₱53,000, what should be the rate of interest for the money borrowed to double in 8 years if the amount is compounding continuously?

To find the rate of interest, r.

The initial amount is P = ₱53,000.

The final amount is, A = 2(53,000) = ₱106,000.

Time period, t = 8 years.

Input all these values in the calculator

A = Pe^rt

100600 = 53000 x e^r(8)

The tool will divide both sides by 53000

Having 2 = e^8r

It will now take "ln" on both sides,

ln 2 = 8r

It will divide both sides by 8,

r = (ln 2) / 8 ≈ 0.087

So, the rate of interest = 0.087 × 100 = 8.7%

**It is easy to use and understand. **Compounding calculators are easy to use and understand, so they are appropriate for anyone, regardless of their financial experience or knowledge, even for people unfamiliar with financial concepts. Unfortunately, most people think of these calculators as complex tools used only by financial professionals.

These calculators often have manual and automatic modes. In manual mode, you need to enter the data individually, while automatic mode automates all calculations for you. For example, suppose that you want to calculate the interest on a loan at 10 % for two years, and then you would have to enter the figures manually. Suppose, though, that you want to calculate how much your investment will be worth in five years. Enter the numbers automatically, and the calculator will do the rest.

**It helps you make informed financial decisions**. Compounding calculators can help you make intelligent financial decisions by showing how different scenarios (for instance, changes in interest rates, investment amounts, and loan terms) could affect your financial future. This can help you make better financial decisions and achieve your long-term goals, and compounding calculators can also help you plan for retirement. A compounding calculator, for example, could help you determine how much money you need to save each month from retiring with a certain amount of savings. When you require a loan, it can also come in handy. For example, suppose you are looking to take out a loan. In this case, you can use a compounding calculator to determine how much the loan will cost, which can help you decide whether the loan is right for you and whether you can afford to repay it.

**It produces accurate results**. Compounding calculators can help you make intelligent financial decisions by showing how different scenarios (for example, changes in interest rates, investment amounts, and loan terms) could affect your financial future. This can help you make better financial decisions and achieve your long-term goals, and compounding calculators can also help you plan for retirement. A compounding calculator, for example, could help you determine how much money you need to save each month from retiring with a certain amount of savings. When you require a loan, it can also come in handy. For example, suppose you are looking to take out a loan. In this case, you can use a compounding calculator to determine how much the loan will cost, which can help you determine whether the loan is right for you and whether you can afford to repay it.

**It helps to understand complex financial concepts**. Compounding calculators can also help you understand complex financial concepts that are difficult to understand without a calculator, such as compound interest. Using a compounding calculator, you can experiment with different scenarios and see how they affect your finances. Compounding calculators make these concepts easier to comprehend, which can help you better manage your finances. This can help you better understand complex financial concepts and make better financial decisions. For example, a compounding calculator can help you understand how compound interest works. This information can help you make more informed decisions about your investments and ensure you get the most out of your money.

**It offers flexibility. **Compounding calculators offer greater versatility, which can benefit people with different financial needs. They are not restricted to a certain set of calculations so that they can be used for various purposes. Compounded calculators are also flexible in how they accept data: you can input the numbers in any order, and the calculator will still give accurate results. For instance, you can select the calculator that best fits your needs and adjust the settings according to your needs. This flexibility can help you choose the right calculator for your financial situation.

Just like the simple interest calculator, there are no special features or functions in this tool; one needs to input the values correctly and then be sure of getting the problem solved in a split of seconds.

Some of the functions one may likely see while using this tool are:

A = total accrued amount ( i.e, principal + interest)

P = the principal amount

I = the interest amount

r = the rate of interest per year in decimal; r = R/100

R = the interest rate per year in percentage; R = r x 100

t = the time in days, months, or number of years

e = mathematical constant where e ≈ 2.7183.

**Compounding frequency**. The compound frequency is the number of times the accumulated interest is credited to the account regularly (or not up to maturity); it could be a year, a half-year, a month, a week, or a daily commitment.

**Principle**. Also known as "the amount taken," it is the sum initially borrowed from the bank or the entire amount infused. P indicates this sum.

**Rate**. This is the interest rate at which the principal amount is repaid to a borrower for a certain period, such as 5 %, 10 %, 15 %, and so on.

A compound interest calculator shows you how much interest your investment or savings may earn over time and gives you a future balance and projected monthly and annual interest breakdown for that time period.

Using the computer's keyboard to input data for this tool is very easy because everything is digital, so there are no special functions to look forward to. Here's how to use the tool:

Firstly, enter an initial balance figure

Then enter a percentage interest rate - either yearly, monthly, weekly, or daily

And then enter several numbers of years or months, or a combination of both, for the calculation

Then you select your compounding interval (daily, monthly, quarterly, or yearly compounding)

And finally, you include any monthly, quarterly, or yearly deposits or withdrawals.

You can then use the results to create a saving strategy to maximize your future wealth.

**Example 1**: Let's say someone has an investment account that increased from ₱30,000 to ₱33,000 over 30 months. If their local bank offers a savings account with daily compounding (365 times per year), what is the annual interest rate they need to get to match the rate of return in their investment account?

In the calculator, select **Calculate rate (R)**. The calculator will then use the equations: r = n[(A/P)^1/nt -1] and R = r x 100.

Enter:

Total P+I (A) = ₱33,000

The principal (P) = ₱30,000

The compound growth(n) = Daily (365)

The time (t in years) = 2.5 years (30 months equals 2.5 years)

Showing the work with the formula r = n[(A/P)^1/nt -1]:

r = 365 [(33,000/30,000)^1/365×2.5 −1]

r = 365(1.1^1/912.5 −1)

r = 365(1.1^0.00109589 −1)

r = 365(1.00010445 −1)

r = 365(0.00010445)

r = 0.03812605

R = r×100 = 0.03812605 × 100 =3.813%

R is 3.813% per year

**Example 2:** A lends ₱4000 to B at an interest rate of 10% per annum, compounded half-yearly for 2 years. Let's see how the calculator can help determine how much A gets after a period of 2 years from B.

Firstly, let us identify the data given to us:

The principal amount, P = ₱4000

Rate of interest, r = 10% per annum.

The conversion period = Half-year

The rate of interest per half-year = 10/2 % = 5%

The number of years, t = 2 years.

**1st half of the year**:

Principal = ₱4000

Interest = 5% × ₱4000 = (5/100) × 4000 = ₱200

Amount = ₱4000 + ₱200 = ₱4200

**2nd half of the year**:

Principal = ₱4200

Interest = 5% × ₱4200 = 5/100 × 4200 = ₱210

Amount = ₱4200 + ₱210 = ₱4410

**3rd half of the year**:

Principal = ₱4410

Interest = 5% × ₱4410 = ₱220.5

Amount = ₱4410 + ₱220.5 = ₱4630.5

**4th half of the year**:

Principal = ₱4630.5

Interest = 5% ×₱$4630.5 = ₱231.53

Amount = ₱4630.5 +₱$231.53 = ₱4862.03

Therefore, the total interest to be paid over 2 years is ₱200 + ₱210 + ₱220.5 + ₱231.53 = ₱862.03. Total amount = P + I = ₱4000 + ₱862.03 = ₱4862.03. So the total amount is ₱4862.03.

₱5,000 is deposited into a savings account at an annual interest rate of 5%, compounded monthly, with additional deposits of ₱100 per month made at the end of each month. The total deposits and value of the investment after 10 years can be calculated using the compound interest calculator as follows:

P = 5000

PMT = 100

r = 5/100 = 0.05 (decimal)

n = 12

t = 10

If we plug those figures into the calculator, we get:

Total value = [ Compounded interest for principal ] + [ Future value of a series ]

= [ P(1+r/n)^(nt) ] + { PMT × [((1 + r/n)^(nt) - 1) / (r/n)] }

= [ 5000 (1 + 0.05 / 12) ^ (12 × 10) ] + { 100 × [((1 + 0.00416)^(12 × 10) - 1) / (0.00416)]}

= [ 5000 (1.00416) ^ (120) ] + { 100 × [((1.00416^120) - 1) / 0.00416]}

= [ 8235.05 ] + [ 100 × (0.647009497690848 / 0.00416) ]

= [ 8235.05 ] + [ 15528.23 ]

= [ ₱23,763.28 ]

Therefore, the investment balance after 10 years is ₱23,763.28