Question

Find the difference between the compound interest compounded yearly and half-yearly for the following: 

Rs 20,000 for ${\displaystyle 1\frac{1}{2}}$ years at 16 %  p.a.

Answer 1

P=Rs 20,000;  t = ${\displaystyle 1\frac{1}{2}}$ years 

When compounded yearly: r = 16% p.a.

${\displaystyle \text{A}=\text{P}{(1+\frac{\text{r}}{100})}^{\text{n}}}$

A = Rs 20000 ${\displaystyle (1+\frac{16}{100}){(1+\frac{16}{100})}^{\frac{1}{2}}}$

= Rs 20000 × 1.16 × ${\displaystyle (1+\frac{1}{2}\times \frac{16}{100})}$

= Rs 20, 000 x 1.16 x 1.08

= Rs 25,056 
C.I. = A - P

= Rs (25,056 - 20,000)

= Rs 5,056 

When compounded half-yearly: 

${\displaystyle \text{A}=\text{P}{(1+\frac{\text{r}}{100})}^{\text{n}}}$

A = Rs 20000 ${\displaystyle {(1+\frac{8}{100})}^3}$

= Rs 20,000 x 1.08 x 1.08 x 1.08

= Rs 25,194.24 

C.l. = A - P

= Rs (25,194.24- 20,000)

= Rs 5,194.24 

Hence the difference in the interest=Rs (5,194.24 - 5,056) = Rs 138.24