Question

The ratio of the amount for 2 years under compound interest annually and for one year under simple interest is in the ratio 6 is to 5. When the rate of interest is the same then the value of the rate of interest is?

Answer 1

The ratio of the amount for 2 years under compound interest annually and for one year under simple interest is in the ratio 6 is to 5. When the rate of interest is the same then the value of the rate of interest is?

Solution:
Let the Principal be Rs 100
time = 2years
Rate = r

Case i) Amount in compound interest = $P[1+ \frac{r}{100}]^n = [tex]100[1+ \frac{r}{100}]^2$

 = $100[\frac{100+r}{100}]^2$

= $[\frac{(100+r)^2}{100}]$

Amount in SI = $\frac{PTR}{100} + P$

= $\frac{100*1*r}{100} + 100 = r +100$

Given ratio= 6 : 5

Therefore, $\frac{(100+r)^2}{100} : r+100 = 6 : 5$

On simplification,

$\frac{(100+r)^2}{100} * 5 = 6(r + 100)$

$\frac{(100+r)^2}{20} = 6r + 600)$

$10000 + r^2 + 200r = 120r + 12000$

$r^2 + 80r - 2000 = 0$

(r + 100) (r - 20) = 0

Therefore, r = 20

Rate of interest = 20%