### Compound Interest - 4

16. What is the principal amount which earns Rs.132 as compound interest for the second year at 10% per annum ?
a. Rs.1000
b. Rs.1200
c. Rs.1320
d. None of these
Correct Option: B
Explanation:
Let x be the principal at the end of first year.
Then $\displaystyle\frac{{x \times 10 \times 1}}{{100}} = 132 \Rightarrow x = 1320$
Let y be the original principal
Then, y + $\displaystyle\frac{{y \times 10 \times 1}}{{100}} = 1320 \Rightarrow y = 1200$

17. A sum amounts to Rs.1352 in 2 years at 4% compound interest. The sum is :
a. Rs.1300
b. Rs.1250
c. Rs.1260
d. Rs.1200
Correct Option: B
Explanation:
Let the sum be P . Then, 1352= P ${\left( {1 + \displaystyle\frac{4}{{100}}} \right)^2}$

$\Rightarrow 1352 = P \times \displaystyle\frac{{26}}{{25}} \times \displaystyle\frac{{26}}{{25}}$

$\Rightarrow P = \displaystyle\frac{{1352 \times 25 \times 25}}{{26 \times 26}} = 1250$

18. The compound interest on Rs.30000 at 7% per annum for a certain time is Rs.4347. The time is :
a. 2 years
b. $2\displaystyle\frac{1}{2}$ years
c. 3 years
d. 4 years
Correct Option: A
Explanation:
$30000 \times {\left( {1 + \displaystyle\frac{7}{{100}}} \right)^t} = 30000 + 4347$
or ${\left( {\displaystyle\frac{{107}}{{100}}} \right)^t} = \displaystyle\frac{{34347}}{{30000}} = \displaystyle\frac{{11449}}{{10000}} = {\left( {\displaystyle\frac{{107}}{{100}}} \right)^2}$
Time = 2 years

19. Rs.800 at 5% per annum compound interest will amount to Rs.882 in :
a. 1 year
b. 2 years
c. 3 years
d. 4 years
Correct Option: B
Explanation:
Let time be t years
$882 = 800{\left( {1 + \displaystyle\frac{5}{{100}}} \right)^t} = \displaystyle\frac{{882}}{{800}} = {\left( {\displaystyle\frac{{21}}{{20}}} \right)^t}$
= ${\left( {\displaystyle\frac{{21}}{{20}}} \right)^2} = {\left( {\displaystyle\frac{{21}}{{20}}} \right)^t} \Rightarrow t = 2$
time = 2 years

20. Simple interest on a sum at 4% per annum for 2 years is Rs.80.The compound interest on the same sum for the same period is :
a. Rs.81.60
b. Rs.160
c. Rs.1081.60
d. None of these
Correct Option: A
Explanation:
Principal = Rs. $\left( {\displaystyle\frac{{100 \times 80}}{{4 \times 2}}} \right)$ = Rs.1000
C.I = Rs. $\left[ {\left\{ {1000 \times {{\left( {1 + \displaystyle\frac{4}{{100}}} \right)}^2} - 1000} \right\}} \right]$ = Rs.81.60

Ramakrishna Salagrama