The compound interest accrued on a sum of Rs. 7,500 in two years is Rs.927. What would be the rate of interest p.c.p.a. ?

P = ₹7,500

C.I. = ₹927

T = 2 years

R = ?

Solution

When the interest is compounded annually

C.I. = $P(1+R/100)^n - 1$

$=> 927 = 7,500{(100+R/100)^2 - 1}$

$=> 927/7,500 = (100+R/100)^2 - 1$

$=> 309/2,500 = (100+R/100)^2 - 1$

$=> 309/2,500 + 1 = (100+R/100)^2$

$=> 309+2,500/2,500 = (100+R/100)^2$

$=> √2,809/2,500 = 100+R/100$

$=> 53/50 = 100+R/100$

$=> 53 × 100 = 50(100+R)$

$=> 5,300 = 5,000 + 50R$

$=> 5,300 - 5,000 = 50R$

$=> 300 = 50R$

$=> R = 300/50$

$=> R = 6 %$ pa

P = ₹7,500

C.I. = ₹927

T = 2 years

R = ?

Solution

When the interest is compounded annually

C.I. = P{(1+R/100)^n - 1}

=> 927 = 7,500{(100+R/100}^2 - 1}

=> 927/7,500 = (100+R/100)^2 - 1

=> 309/2,500 = (100+R/100)^2 - 1

=> 309/2,500 + 1 = (100+R/100=^2

=> 309+2,500/2,500 = (100+R/100)^2

=> √2,809/2,500 = 100+R/100

=> 53/50 = 100+R/100

=> 53 × 100 = 50(100+R)

=> 5,300 = 5,000 + 50R

=> 5,300 - 5,000 = 50R

=> 300 = 50R

=> R = 300/50

=> R = 6 % pa