Question

A person deposited 5,000 in a
bank. The deposit was left to
accumulate at 6% compounded
quarterly for the first five years and
at 8% compounded semi-annually
for the next eight years. The
compound amount at the end of 13
years is :​

Answer 1

The answer is 12,613.16

Answer 2

Therefore the compound amount at the end of 13 years is Rs. 12,615/-

Given:

The principal amount = P = Rs. 5,000/-

Rate of interest compounded quarterly for first 5 years = 6%

Rate of interest compounded semi-annually for next 8 years = 8%

The period for the first 5 years = 20 quarters

Period for next 8 years = 16 half years

To Find:

The compound amount is at the end of 13 years.

Solution:

The given question can be solved as shown below.

Let n be the number of intervals.

For the first 5 years:

The number of intervals = 4 ( There are 4 quarters in a year )

Compound amount = P [ 1 + R/n100 $]^n^T$

⇒ Compound amount = 5,000 ( 1 + 0.015 )²⁰

⇒ Compound amount = 5,000 ( 1.015 )²⁰ = Rs. 6735/-

For the next 8 years:

The number of intervals = 2 ( There are 2 semi-annual intervals in a year )

Compound amount = P [ 1 + R/n100 $]^n^T$

⇒ Compound amount = 6735 ( 1 + 0.04 )¹⁶

⇒ Compound amount = 6735 ( 1.04 )¹⁶ = Rs. 12,615/-

Therefore the compound amount at the end of 13 years is Rs. 12,615/-

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