Let us learn in detail how to calculate **compound interest** with the growing principal in this article. If the Interest is due at the end of a certain period be it after a year, half-year, quarterly duration, etc. to a moneylender then Interest is added to the sum borrowed. Thus, Amount becomes the Principal for the next period of borrowing. The Procedure continues further till the specific time is found.

Refer to the Solved Examples on finding Compound Interest with Growing Principal and understand the concept better. We have provided step by step solutions for all the Compound Interest with Increasing Principal Problems.

## Solved Examples on Compound Interest with Growing Principal

1. A man takes a loan of $ 20,000 at a compound interest rate of 5% per annum.

(i) Find the amount after 1 year?

(ii) Find the compound interest for 2 years?

(iii) Find the amount required to clear the debt at the end of 2 years?

Solution:

(i) Given P = $20, 000, R = 5%, T = 1 year

We know the Formula for Amount A = P(1+R/100)^{n}

Substitute the given input data in the formula to obtain the amount

A = 20000(1+5/100)^{1}

= 20000(1+0.05)

= 20000(1.05)

= 21000

Amount to be paid after 1 year is $21, 000.

SI = A – P

= 21, 000 – 20, 000

= $1, 000

(ii) For Second Year New Principal = $21,000

Thus, Interest in Second Year = 5% of 21, 000

= 5/100*21, 000

= $1050

Compound Interest for 2 Years = Interest of 1st Year + Interest of 2nd Year

= $1000+$1050

= $2050

(iii) Amount required to clear the debt at the end of 2 years = Principal + Compound Interest for 2 Years

= $20, 000 + $2050

= $22, 050

2. At 8% per annum, find the compound interest for 2 years on a certain sum of money?

Solution:

Let the sum be x

Interest for 1st year = 8% of x

= 8x/100

Amount after 1 year = Principal + Interest after 1 year

= x+8x/100

= 108x/100

For second-year New Principal is 108x/100

Interest for 2nd Year = 8% of 108x/100

= 8/100*108x/100

=864x /10000

Amount after 2 years = Principal + Interest after 2 Years

= x +864x/100

= 964x/100

CI = Interest for 1st year + Interest for 2nd Year

=8x/100 + 864x /10000

= 8x/100+54x/625

= (200x+216x)/2500

= 416x/2500

= 104x/625

3. Calculate the compound interest to be paid on a loan of Rs. 5000 for 5/2 years at 10% per annum compounded half-yearly?

Solution:

From the given data Principal = Rs. 5000

T = 5/2

R = 10%

A = P(1+R/100)^{n}

When Interest is Compounded Half Yearly we need to multiply T with 2 and divide R with 2 thus equation becomes as such

A = 5000(1+10/2*100)^{2*5/2}

= 5000(1+5/100)^{5}

= 5000(105/100)^{5}

= 5000(1.2762)

= 6381

CI = A – P

= 6381 – 5000

= Rs. 1381

Therefore, Compound Interest on a sum Rs. 5000 for 5/2 years at 10%, when compounded half-yearly, is Rs. 1381.