Compound Interest 1/5

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25. The compound interest on a certain sum of money for 2 years at 10% per annum is Rs.420. The simple interest on the same sum at the same rate and for the same time will be :
a. Rs.350
b. Rs.375
c. Rs.380
d. Rs.400

Answer: D

Explanation:
Let principal be P. Then, $P\left( {1 + {{\displaystyle\frac{P}{{100}}}^2}} \right) - P = 420 \Rightarrow P $=Rs.2000
S.I = Rs.$\displaystyle\frac{{2000 \times 2 \times 10}}{{100}}$= Rs.400

26. The difference between the compound interest and simple interest on a certain sum at 5% per annum for 2 years is Rs.1.50. The sum is :
a. Rs.600
b. Rs.500
c. Rs.400
d. Rs.300

Answer: A

Explanation:
Let the sum be Rs. 100. Then.
S.I = Rs. $\left( {\displaystyle\frac{{100 \times 5 \times 2}}{{100}}} \right)$ = Rs.10
C.I = Rs.$\left[ {\left\{ {100 \times {{\left( {1 + \displaystyle\frac{5}{{100}}} \right)}^2}} \right\} - 100} \right]$ = Rs. $\displaystyle\frac{{41}}{4}$
Difference between C.I and S.I. = Rs. $\left( {\displaystyle\frac{{41}}{4} - 10} \right)$=Rs.0.25
0.25 : 1.50 : : 100 : x
x = $\displaystyle\frac{{1.50 \times 100}}{{0.25}}$= Rs.600

27. A sum of money placed at C.I doubles itself in 5 years. It will amount to eight times itself in :
a. 15 years
b. 20 years
c. 12 years
d. 10 years

Answer: A

Explanation:
Let the principal P and rate be r% . Then, 2P = P ${\left( {1 + \displaystyle\frac{r}{{100}}} \right)^5}$ or
${\left( {1 + \displaystyle\frac{r}{{100}}} \right)^5}$ = 2
Let it be 8 times in t years . Then, 8p = p ${\left( {1 + \displaystyle\frac{r}{{100}}} \right)^t}$
or ${\left( {1 + \displaystyle\frac{r}{{100}}} \right)^t}$=8=${(2)^3}$ = ${\left( {{{\left( {1 + \displaystyle\frac{r}{{100}}} \right)}^5}} \right)^3} = {\left( {1 + \displaystyle\frac{r}{{100}}} \right)^{15}}$
t = 15 years

28. The simple interest on a certain sum for 2 years at 10% per annum is Rs.90. The corresponding compound interest is :
a. Rs.99
b. Rs.95.60
c. Rs.94.50
d. Rs.108

Answer: C

Explanation:
Sum = Rs. $\left( {\displaystyle\frac{{100 \times 190}}{{2 \times 10}}} \right)$ = Rs.450
C.I = Rs. $\left[ {450 \times {{\left( {1 + \displaystyle\frac{{10}}{{100}}} \right)}^2} - 450} \right]$ = Rs.94.50

29. 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

Answer: B

Explanation:
Let x be the principal at the end of first year.
So interest on first year ending amount = $\displaystyle\frac{{x \times 10 \times 1}}{{100}} = 132 \Rightarrow x = 1320$
Let y be the original principal. Then one year interest + principal = 1320
So, y + $\displaystyle\frac{{y \times 10 \times 1}}{{100}} = 1320 \Rightarrow y = 1200$

30. 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

Answer: 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$

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