Compounding Formula

Compounding Formula Calculation

Compounding formula is used to calculate total interest on the principal earned when the interest amount which is earned and reinvested and is calculated by principal amount multiplied by one plus rate of interest raise to the power number of periods less principal amount.

Where,

• C is the compound interest
• P is the principal amount
• r is the rate of interest
• n is the number of periods

Explanation

It is very useful and is powerful when one wants to calculate compound interest. This equation takes into consideration the principal amount, the rate of interest, the frequency at which it shall pay an interest rate. The equation in itself compounds the interest amount, which is earned and reinvested. This gives the effect of multiplication, and the amount grows more than what growth it achieved in the earlier years. Hence, this is more powerful than the simple interest, which only pays with the same amount of interest every year.

Examples

Example #1

Mr. V deposited $100,000 in HFC bank for 2 years, and the bank pays 7% interest, which is compounded annually. You are required to compute the compounded interest amount.

Solution

 All of the variables that are required in the formula are given

• Principal Amount: 100000.00
• Rate of Interest: 7.00%
• Number of Years: 2.00
• Frequency: 1.00

Therefore, calculation of compound interest can be done using the above equation as,

• =  100,000 [ (1+7%)² – 1 ]
• =   100,000 [ (1.07)² – 1 ]

Compound Interest will be –

• Compound Interest = 14,490.00

Hence, the amount of interest will be 14,490 on the amount invested.

Example #2

KBC Bank has just launched a new product to compete with the existing market product. They believe this would be the winning game for them. Below are the details of both of the schemes. Mr. W was interested in investing in New Scheme as he was shown by the bank that the interest amount he would earn at maturity would be 37,129.99 and 52,279.48 on the existing scheme and a new scheme. You are required to validate the statement made by the banker.

Particulars	Existing Scheme	New Scheme
Principal Amount	100000.00	100000.00
Rate of Interest	7.92%	8.50%
Number of Years	4	5
Frequency	12.00	4

Solution

Here, we need to make a comparison of the schemes, and Mr. W will surely get lured by seeing the difference of interest earned. However, there is a mismatch in several years and hence cannot be compared to the interest of 37,129.99 verses 52,279.48 as one is for four years, and the other one is for five years. Hence, we will calculate the compound interest for four years.

Existing Scheme

Therefore, the calculation of compound interest for the existing scheme can be done as follows,

• = 100,000 [ (1+(7.92%/12))^(4*12) – 1 ]
• =   100,000 [ (1.0198)⁴⁸ – 1 ]

Compounding Interest of Existing Scheme will be –

• Compound Interest = 37,129.99

New Scheme

Therefore, calculation of compound interest for the new scheme can be done as follows,

• =  100,000 [ (1+(8.50%/4)^(5*4) – 1 ]
• =  100,000 [ (1.02125)⁴⁸ – 1 ]

Compounding Interest of New Scheme will be –

• Compound Interest = 52279.48

As we can see, the difference is not that many majors, but as we can see, the difference is of approx. 15149.5 and further, there is one year more of the lock-in period. Hence, it’s up to Mr. W whether he requires funds in 4 years, and then he can go for the existing scheme, and it appears that the bank is luring customers by displaying such a high value of interest difference and lock funds with the bank for one more year.

Example #3

Mr. Vince is interested in purchasing the house, but he does not want to take a loan burden. He learns about Mutual funds in an advertisement, and he is keen to know that on an average, the return on a mutual fund is 10-12% if kept invested for ten years or more. The house that he wants to purchase is valued at 5,000,000. Hence, he approaches financial advisors to know what amount he should invest every month to reach the goal. The financial advisor takes 11.50% as an annual interest rate compounding monthly and considers staying invested for 12 years one-time investment of 1,700,000. You are required to compute the income earned on the investment if Mr. Vince stays invested for 12 years.

Solution

We are given all the details here, and we can use the below formula to calculate the income that will be derived by investing 10,000 monthly for 12 years at a rate of 11.50% compounded monthly.

• Principal Amount (P): 1700000.00
• Rate of Interest (r): 11.50%
• Number of Years (n): 12.00
• Frequency: 12.00

Therefore, calculation of compound interest can be done using the above formula as,

• = 1,700,000 [ (1+(11.50%/12)^(12*12) – 1 ]
• = 1,700,000 [ (1.02125)¹⁴⁴ – 1 ]

Compound Interest will be –

• Compound Interest= 50,13,078.89

Hence, if Mr. Vince stays invested for 12 years, he would be able to reach his goal of buying the house, assuming he earns 11.50%.

Relevance and Uses

It is used in many instances, like for calculating recurring fixed deposit income, mutual fund returns, also in capital markets like in growth in sales, profit, etc. by financial analysts. It looks simple, but the effect it has is very large in the longer term. Many of the banks use compounding in their housing loans, vehicle loans, education loans, which are the major chunk of the revenue sources. The power of compounding can make one wealthy in the long term.

Recommended Articles

This article has been a guide to Compounding Formula. Here we discuss step by step how to calculate compound interest using its formula along with practical examples and a downloadable excel template. You can learn more from the following articles –

• Capital Market Advantages & Disadvantages
• Formula of Continuous Compounding
• Daily Compound Interest
• Formula of CAGR