Finance

# 3 important formulae that you should know about – Compound interest, CAGR and annuity calculator

Proper knowledge and prudent management of personal finances play an important role in wealth appreciation and financial analysis. Besides giving you a sense of independence, these also help you plan your finances according to your financial goals. In this article, we talk about the three most essential formulae that you should know while planning your investments, especially when it comes to shares and mutual funds.

## 1. Compound interest

It refers to a cumulative interest amount calculated on your principal deposit/loan amount and the interest earned/payable on it during its tenure. It is a very powerful formula in the sense that it calculates interest even on the accrued interest.

Compound interest formula:

 Compound interest =  P(1+r/n)^nt – P

Where,

P = Principal amount

r = Rate of interest in percentage terms

n = Number of times the interest is compounded in a year

t = Tenure of deposit/loan

Example –

Mr A deposits Rs. 50,000, which bears a compound interest of 10% p.a. and a tenure of 5 years.

Interest earned by Mr. A after 5 years = 50,000 (1+0.1/1)^(5*1) – 50,000 = Rs. 30,525.5 (in contrast to a simple interest of Rs. 25,000).

## 2. CAGR

Compound Annual Growth Rate (CAGR) refers to an annualised average rate of return on an investment over a certain period. It is calculated while taking into account the effect of compounding. It comes in handy while comparing two different investment, say the performance of a stock versus a mutual fund plan.

CAGR formula:

 CAGR = (A/P)^1/t – 1

Where,

A = Amount at the end of investment period

P = Principal amount

t = Tenure of investment

Example –

Mr. A invested Rs. 20,000 in a mutual fund which grew to Rs. 29,000 in 3 years. So, Mr. A earned a CAGR of 13.04% [(29,000/20,000)^⅓ – 1].

## 3. Annuity calculator

An annuity is a financial instrument that pays you a fixed sum of money annually in return for a series of deposits made over a certain period.

Annuity Formula:

 A = P * [{(1+r)^n – 1 }/r]

Where,

A = Amount at the end of investment period

P = Principal amount

r = Rate of return in percentage terms

n = Number of deposit payments

Example –

Mr. A makes mutual fund investments in monthly SIPs of Rs. 5,000 for 5 years. The mutual fund is expected to provide a return of 24% p.a. So, he shall receive an amount in accordance with the following:

r = 2% (24%/12, as SIPs are made monthly)

n= 5 years * 12 months = 60 months

A = 5,000*[{(1+0.02)^60-1}/0.02] ~ 5,70,257

It is good to know varying personal finance terms inside out for robust financial planning. But, it is always better to seek expert advice for your finances so that you can accomplish your financial aspirations while keeping in mind your risk appetite. An expert can not only help you with sound advice but also suggest different avenues like mutual fund investments, exchange traded funds, etc. as per your goals and risk tolerance.