Compound Interest 1/6

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31. 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

Answer: C

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

32. 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

Answer: 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

33. 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

Answer: 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

34. The difference of compound interest on Rs.800 for 1 year at 20% per annum when compounded half-yearly and quarterly is :
a. Nil
b. Rs.2.50
c. Rs.4.40
d. Rs.6.60

Answer: C

Explanation:
C.I when reckoned half-yearly
= Rs. $\left[ {800 \times {{\left( {1 + \displaystyle\frac{{10}}{{100}}} \right)}^4} - 800} \right]$ = Rs. 172.40
Difference = Rs.(172.40-168) Rs.4.40

35. The difference between simple interest and the compound interest on Rs.600 for 1 year at 10% per annum, reckoned half-yearly is :
a. Nil
b. Rs.6.60
c. Rs.4.40
d. Rs.1.50

Answer: D

Explanation:
S.I = Rs. $\left( {\displaystyle\frac{{600 \times 10 \times 1}}{{100}}} \right)$ = Rs.60
C.I = Rs. $\left[ {600 \times {{\left( {1 + \displaystyle\frac{5}{{100}}} \right)}^2} - 600} \right]$ = Rs.61.50
Difference = Rs.(61.50-60) = Rs.1.50

36. The compound interest of Rs.20480 at $6\displaystyle\frac{1}{4}$% per annum for 2 years 73 days is :
a. Rs.3000
b. Rs.3131
c. Rs.2929
d. Rs.3636

Answer: C

Explanation:
73 days is 1/5 th of an year. So interest would be 1/5th of the rate of interest for the 73 days.
A = \({20480 \times {{\left( {1 + \dfrac{{{\textstyle{{25} \over 4}}}}{{100}}} \right)}^2}\left( {1 + \dfrac{{\left( {{\textstyle{1 \over 5}} \times {\textstyle{{25} \over 4}}} \right)}}{{100}}} \right)}\)
= \({20480 \times {{\left( {1 + \dfrac{1}{{16}}} \right)}^2}\left( {1 + \dfrac{1}{{80}}} \right)}\)
= \({20480 \times {{\left( {\dfrac{{17}}{{16}}} \right)}^2}\left( {\dfrac{{81}}{{80}}} \right)}\)
= 23409
Compound interest = 23409 - 20480 = Rs.2929

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