Question

Swati borrowed $Rs.40960$ from a bank to buy a piece of land. If the bank charges $12\frac{1}{2}$% per annum compound half-yearly, what amount will she have to pay after $1\frac{1}{2}$ years? Also find the interest paid by her.

Answer 1

The formula for compound interest, including principal sum, is:
A = P (1 + r/n)^ (nt)

Where:

• A = the future value of the investment/loan, including interest
• P = the principal investment amount (the initial deposit or loan amount)
• r = the annual interest rate (decimal)
• n = the number of times that interest is compounded per unit t
• t = the time the money is invested or borrowed for

In our given problem,

P = Rs. 40960

r = 12.5% = 0.125

n = 2

t = 1.5 years

Therefore, the amount payable after the term of 1.5 years will be given by: A = P (1 + r/n)^ (nt)

A = 40960 (1 + 0.125/2) ^(2×1.5)

A = 40960 (1 + 0.0625)^ 3

= 40960 (1.0625) ^3

A = ₹ 49130

The interest payable is given by I = A - P

I = 49130 - 40960

I = ₹ 8170