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SSC CGL Tier1 Quantitative Aptitude Interest Test 5

2581.The difference between simple interest and compound on Rs. 900 for one year at 10% per annum reckoned half-yearly is:
Rs. 3
Rs. 2.25
Rs. 4.5
Rs. 4
Explanation:

Simple Interest =$\dfrac{PRT}{100}$ = $\dfrac{900 \times 10 \times 1}{100} $= Rs.90

Amount after 1 year on Rs.900 at 10% per annum when interest is reckoned half-yearly

=P $\left(1 + \dfrac{\left(R/2\right)}{100}\right)^2T$ = 900$\left(1 + \dfrac{(10/2)}{100}\right)^{2 \times 1}$ = 900$\left(1 + \dfrac{5}{100}\right)^{2}$ = 900$\left(\dfrac{105}{100}\right)^{2}$

$= \dfrac{900\times 105 \times 105}{100 \times 100}$ = Rs.992.25

Compound Interest = 992.25 - 900 = 92.25

Required difference between simple interest and compound interest = 92.25 - 90 = Rs.2.25

2582.The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
6.06%
6.07%
6.08%
6.09%
Explanation:
Amount of Rs. 100 for 1 year
when compounded half-yearly= Rs $\left[100\times\left(1+\dfrac{3}{100}\right)^2\right]$= Rs. 106.09

$\therefore$ Effective rate = (106.09 - 100)% = 6.09%

2583.A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:
Rs. 120
Rs. 121
Rs. 122
Rs. 123
Explanation:

= Rs. $\left[1600\times\left(1+\dfrac{5}{2\times100}\right)^2+1600\times\left(1+\dfrac{5}{2\times100}\right)\right]$

= Rs. $\left[1600+\dfrac{41}{40}\times\dfrac{41}{40}+1600\times\dfrac{41}{40}\right]$

= Rs. $\left[1600+\dfrac{41}{40}\left(\dfrac{41}{40}+1\right)\right]$

= Rs. $\left[\dfrac{1600\times41\times81}{40\times40}\right]$

= Rs. 3321

$\therefore$ C.I. = Rs. (3321 - 3200) = Rs. 121

2584.What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 11 p.c.p.a.?
Rs. 14705.24
Rs. 14602.25
Rs. 14822.26
Rs. 14322.10
Explanation:

Amount after 3 years = P $\left(1 + \dfrac{R}{100}\right)^T$ = $40000\left(1 + \dfrac{11}{100}\right)^3$ =$ 40000\left(\dfrac{111}{100}\right)^3$

= $\dfrac{40000 \times 111 \times 111 \times 111}{100 \times 100 \times 100}$ = $\dfrac{4\times 111 \times 111 \times 111}{ 100} $= 54705.24

Compound Interest = 54705.24 - 40000 = Rs. 14705.24

2585.At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
6%
6.5%
7%
7.5%
Explanation:

Let the rate be R% p.a.

Then, 1200 $ \times\left(1 +\dfrac{R}{100} \right)^2$= 1348.32
$\Rightarrow \left(1 +\dfrac{R}{100} \right)^2$=$ \dfrac{134832}{120000} $=$ \dfrac{11236}{10000} $
$\therefore \left(1 +\dfrac{R}{100} \right)^2$=$ \left(\dfrac{106}{100} \right)^2$
$\Rightarrow$ 1 +$ \dfrac{R}{100} $=$ \dfrac{106}{100} $

$\Rightarrow$ R = 6%

2587.There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?
Rs. 2160
Rs. 3120
Rs. 3972
Rs. 6240
Explanation:

Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.

$\therefore$ R =$ \left(\dfrac{100 \times 60}{100 \times 6} \right) $= 10% p.a.

Now, P = Rs. 12000. T = 3 years and R = 10% p.a.

$\therefore$ C.I. = Rs.$ \left[12000 \times\left\{\left(1 +\dfrac{10}{100} \right)^3- 1\right\}\right] $
= Rs.$ \left(12000 \times\dfrac{331}{1000} \right) $
= 3972.
2591.What is the difference between the compound interests on Rs. 5000 for 1$ \dfrac{1}{2} $ years at 4% per annum compounded yearly and half-yearly?
Rs. 2.04
Rs. 3.06
Rs. 4.80
Rs. 8.30
Explanation:
C.I. when interest is
compounded half-yearly
= Rs.$ \left[5000 \times\left(1 +\dfrac{4}{100} \right)\times\left(1 +\dfrac{\dfrac{1}{2} \times 4}{100} \right)\right] $
= Rs.$ \left(5000 \times\dfrac{26}{25} \times\dfrac{51}{50} \right) $
= Rs. 5304.
C.I. when interest is
compounded half-yearly
= Rs.$ \left[5000 \times\left(1 +\dfrac{2}{100} \right)^3\right] $
= Rs.$ \left(5000 \times\dfrac{51}{50} \times\dfrac{51}{50} \times\dfrac{51}{50} \right) $
= Rs. 5306.04

$\therefore$ Difference = Rs. (5306.04 - 5304) = Rs. 2.04

44153.Find compound interest on Rs.2500 invested at 6% per annually, compound semi-annually for 8 years.
151.33
1511.73
155.73
1500.32
Explanation:

Let Principal = 2500, r=6%=0.06616=0.03, n=8×2=16

We know that
A=P(1+r)n
=2500(1+.03)16
=4011.73
The compound interest =4011.73−2500=1511.73
44155.If the present value of my investment is $2,500 and the rate of interest is 2% compounded annually, what will the value be after 15 years?
$3,364.67
$3,306.25
$3,250
$3,047.49
Explanation:
Use the formula:
FV = PV × (1 + r)n
Substitute PV = $2,500, r = 2% = 0.02 and n = 15
FV = $2,500 × (1 + 0.02)15 = $2,500 × (1.02)15
= $2,500 × 1.34586...
= $3364.6708...
So the value after 6 years = $3,364.67
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