Let us discuss how to find the Compound Interest when a Variable Rate is given. Check out the Solved Examples on finding the Compound Interest When Rate of Successive Years is Different. We tried explaining each and every step for all the Problems provided here. Use the Problems over here and learn the concept behind them in no time. After going through this article, you will learn the concept of Variable Rate of Compound Interest quite easily.

How to find Compound Interest When Successive Years Rate of Interest is Different?

Get to know in detail how to find the Compound Interest when Consecutive/ Successive Years Rate of Interest is Different from the below sections.

Let us consider the amount be A and Principal be P,

Rate of Compound Interest for Successive Years is different i.e. r1%, r2%, r3%, r4%, …… then the Formula to calculate amount is given by

A = P(1+r1/100)(1+r2/100)(1+r3/100)(1+r4/100)……

Where A = Amount

P = Principal

r1%, r2%, r3%, r4%, ……  are the rate of successive years

Solved Problems on Variable Rate of Compound Interest

1. Find the compound interest accrued by Amar from a bank on $ 12000 in 3 years, when the rates of interest for successive years are 8%, 10%, and 12% respectively?

Solution:

Formula for Amount A = P(1+r1/100)(1+r2/100)(1+r3/100)(1+r4/100)……

From given data P = $12,000

n = 3 years

r1 = 8% r2= 10% r3 = 12%

A = 12,000(1+8/100)(1+10/100)(1+12/100)

= 12,000(1+0.08)(1+0.1)(1+0.12)

= 12,000(1.08)(1.1)(1.12)

= $15966

CI = A – P

= 15966 – 12000

= $3966

2. A company offers the following growing rates of compound interest annually to the investors on successive years of investment 5%, 6% and 7%

(i) A man invests $ 30,000 for 2 years. What amount will he receive after 2 years?

(ii) A man invests $ 20,000 for 3 years. What amount he will receive after 3 years?

Solution:

Formula to Calculate the Amount is A = P(1+r1/100)(1+r2/100)(1+r3/100)(1+r4/100)……

(i) Principal = $30,000

n = 2 years

r1 = 5%, r2 = 6%

Substitute the input values in the formula we have the equation as under

A = 30,000(1+5/100)(1+6/100)

= 30,000(1.05)(1.06)

= $ 33,390

Therefore, the Man receives $33,390 by the end of 2 years.

(ii) From the given data

Principal = $20,000

n = 3 years

r1 = 5%, r2 = 6%, r3 = 7%

Substitute the input values in the formula we have the equation as under

A = 20,000(1+5/100) (1+6/100)(1+7/100)

= 20,000(1.05)(1.06)(1.07)

= $23,818

Therefore, the Man receives $23,818 by the end of 3 years.