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Aptitude Compound Interest Practice QA

2593.The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
8
10
12
Cannot be determined
Explanation:
$ \left[15000 \times\left(1 +\dfrac{R}{100} \right)^2- 15000\right]-\left(\dfrac{15000 \times R \times 2}{100} \right) $= 96
$\Rightarrow$ 15000$ \left[\left(1 +\dfrac{R}{100} \right)^2- 1 -\dfrac{2R}{100} \right] $= 96
$\Rightarrow$ 15000$ \left[\dfrac{(100 + R)^2 - 10000 - (200 \times R)}{10000} \right] $= 96
$\Rightarrow$ R2 =$ \left(\dfrac{96 \times 2}{3} \right) $= 64

$\Rightarrow$ R = 8.

$\therefore$ Rate = 8%.

2594.At what rate of compound interest per annum will a sum of Rs. 1400 become Rs. 1573.04 in 2 years?
4%
5%
6%
8%
Explanation:

Let the rate be R% per annum

$ P\left(1 + \dfrac{R}{100}\right)^T $= 1573.04

$ 1400\left(1 + \dfrac{\text{R}}{100}\right)^2$ = 1573.04

$\left(1 + \dfrac{R}{100}\right)^2$ =$ \dfrac{1573.04}{1400}$ = $\dfrac{157304}{140000}$ = $\dfrac{11236}{10000}$

$\left(1 + \dfrac{R}{100}\right) $= $\sqrt{\dfrac{11236}{10000}}$ = $\dfrac{\sqrt{11236}}{\sqrt{10000}}$ =$\dfrac{106}{100} $

$\dfrac{R}{100} $= $ \dfrac{106}{100} - 1 $=$ \dfrac{6}{100}$

R = 6%

2595.The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum in Rs. is:
625
630
640
650
Explanation:

Let the sum be Rs. $ x $. Then,

C.I. =$ \left[x\left(1 +\dfrac{4}{100} \right)^2- x\right] $=$ \left(\dfrac{676}{625} x- x\right) $=$ \dfrac{51}{625} x $.

S.I. =$ \left(\dfrac{x \times 4 \times 2}{100} \right) $=$ \dfrac{2x}{25} $.

$\therefore \dfrac{51x}{625} $-$ \dfrac{2x}{25} $= 1

$\Rightarrow x $ = 625.

2596.Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:
Rs. 1550
Rs. 1650
Rs. 1750
Rs. 2000
Explanation:
C.I. = Rs.$ \left(4000 \times\left(1 +\dfrac{10}{100} \right)^2- 4000\right) $
= Rs.$ \left(4000 \times\dfrac{11}{10} \times\dfrac{11}{10} - 4000\right) $
= Rs. 840.
$\therefore$ Sum = Rs.$ \left(\dfrac{420 \times 100}{3 \times 8} \right) $= Rs. 1750.
2597.If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?
Rs. 51.25
Rs. 52
Rs. 54.25
Rs. 60
Explanation:
Sum = Rs.$ \left(\dfrac{50 \times 100}{2 \times 5} \right) $= Rs. 500.
Amount = Rs.$ \left[500 \times\left(1 +\dfrac{5}{100} \right)^2\right] $
= Rs.$ \left(500 \times\dfrac{21}{20} \times\dfrac{21}{20} \right) $
= Rs. 551.25

$\therefore$ C.I. = Rs. (551.25 - 500) = Rs. 51.25

2598.The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:
Rs. 2.50
Rs. 3
Rs. 3.75
Rs. 4
Explanation:
S.I. = Rs$ \left(\dfrac{1200 \times 10 \times 1}{100} \right) $= Rs. 120.
C.I. = Rs.$ \left[1200 \times\left(1 +\dfrac{5}{100} \right)^2- 1200\right] $= Rs. 123.

$\therefore$ Difference = Rs. (123 - 120) = Rs. 3.

2599.The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:
Rs. 400
Rs. 500
Rs. 600
Rs. 800
Explanation:

Let the sum be Rs. P.

Then,$ \left[P\left(1 +\dfrac{10}{100} \right)^2- P\right] $= 525
$\Rightarrow$P$ \left[\left(\dfrac{11}{10} \right)^2- 1\right] $= 525
$\Rightarrow$ P =$ \left(\dfrac{525 \times 100}{21} \right) $= 2500.

$\therefore$ Sum = Rs . 2500.

So, S.I. = Rs.$ \left(\dfrac{2500 \times 5 \times 4}{100} \right) $= Rs. 500
2600.A sum amounts to Rs. 882 in 2 years at 5% compound interest. The sum is
Rs. 800
Rs. 822
Rs. 840
Rs. 816
Explanation:

Let the sum be P

Amount After 2 years = P$\left(1 + \dfrac{R}{100}\right)^T$ = P$\left(1 + \dfrac{5}{100}\right)^2$=P$ \left(\dfrac{105}{100}\right)^2$=P$\left(\dfrac{21}{20}\right)^2$

Given that amount After 2 years = 882

=> P$\left(\dfrac{21}{20}\right)^2$ = 882

=> P = $\dfrac{882 \times 20 \times 20}{21 \times 21} = 2\times 20 \times 20 = Rs.800$

44163.You have 1,000, and want it to grow to 2,000 in 4 years, what compound interest rate do you need?
11.89%
18.92%
25%
41.42%
Explanation:
Use the formula:PV=$[\dfrac{(PV)^{\dfrac{1}{n}}}{FV}]-1$
substitute FV=2000 ,PV=1,000 and n=4
therefore r=$[\dfrac{(1000)^{\dfrac{1}{4}}}{FV}]-1$
=$(2)^1/4 -1$
=1.1892-1
=0.1892
=18.92%
44165.You have 2,500, and want it to grow to 4,000 in 10 years, what compound interest rate do you need?
4.81%
6%
6.05%
7.18%
Explanation:
Use the formula:PV=$[\dfrac{(PV)^{\dfrac{1}{n}}}{FV}]-1$
substitute FV=4000 ,PV=2,500 and n=10
therefore r=$[\dfrac{(2,500)^{\dfrac{1}{n}}}{4,000}]-1$
=$(1.6)^0.1 -1$
=1.0481-1
=0.0481
=4.81%
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