Question

Arif took a loan of ₹ 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 1 1/2 years, if the interest is 

(i) compounded annually 

(ii) compounded half yearly.

Answer 1

P = ₹ 80,000; R = 10%; 

T = 1 year

∴ PTR / 100 =  \(\frac{80000\,\times\,10\,\times1}{100}\)

= ₹8000 

∴ A = P + I = 80000 + 8000 

= ₹ 88,000

Interest on 6 months : P = 88,000 ; R = 10% ; T = 6 Months = 1/2 year

 I = PTR / 100  = \(\frac{88000\,\times\,\frac12\,\times10}{100}\) = 4400

i) The amount to be paid after 1 year 6 months = P + I 

= 88000 + 4400 

A₁ = ₹ 92,400

ii) He has to pay compounded on every 6 months in 1 1/2 years 

∴ 3 time periods will be occurred. 

∴ n = 3 

R = 10/2 = 5% P = ₹ 80,000

A₂ = ₹ 92610 

∴ Difference between the amounts = A₂ – A₁ = 92610 – 92400 

= ₹ 210