Question

a sum of 3600 is deposited in a bank and it becomes 3969 in a time period of 6 month find rate of interest per annum if it is compounded quarterly?

Answer 1

Given:

A sum of 3600 is deposited in a bank and it becomes 3969 in a time period of 6 month

To find:

The rate of interest per annum

Solution:

According to the question, the interest is compounded annually.

Principal = Rs. 3600,

Amount = Rs. 3696

Time period = 6 months = 2 cycle

• $A = P(1+\frac{R}{100})^{T}$
• $3696 = 3600(1+\frac{R}{100})^{2}$
• $\frac{3696}{3600}=(1+\frac{R}{100})^{2}$
• $\sqrt{\frac{3696}{3600}} =(1+\frac{R}{100})$
• $\frac{63}{60} = (1+\frac{R}{100})$
• $1+\frac{3}{60} = (1+\frac{R}{100})$
• $1+\frac{1}{20} = (1+\frac{R}{100})$
• $1+\frac{5}{100} = (1+\frac{R}{100})$

on comparing we get

R = 5% but this is for the 3 months only,

The Rate of interest annually is given by:

5×4 = 20%

So the rate of interest per annum is 20%