Test: Compound Interest- 1
10 Questions MCQ Test CSAT Preparation for UPSC CSE | Test: Compound Interest- 1
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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:
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.?
Amount after 3 years = P(1 + R/100)T
=> 40000(1 + 11/100)3
=> 40000(111/100)3
=> 40000[(111*111*111)/(100*100*100)]
=> (4*111*111*111)/100
=> 54705.24
Compound Interest = 54705.24 - 40000
= Rs. 14705.24
Q. What is the difference between the compound interests on Rs. 5000 for 11/2 years at 4 percent per annum compounded yearly and half yearly?
If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 60, what is the compound interest on the same at the same rate and for the same time?
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?
[15000×(1+R/100)2 − 15000] - (15000×R×2)/100 = 96
⇒15000[(1+R/100)2 − 1 − 2R/100]=96
⇒ 15000[(100+R)2 − 10000−(200×R)]/10000 = 96
⇒ R2 = (96×23) = 64
⇒ R = 8
∴ Rate = 8%
The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:
Amount = Rs.(30000+4347) = Rs.34347
let the time be n years
Then,30000(1+7/100)n = 34347
(107/100)n = 34347/30000
= 11449/10000
= (107/100)2
n = 2years
At what rate of compound interest per annum will a sum of Rs. 1400 become Rs. 1573.04 in 2 years?
Let the rate be R% per annum
P(1+R/100)T = 1573.04
= 1400(1+R/100)2 = 1573.04
= (1+R/100)2 = 1573.04/1400 = 157304/140000 = 11236/10000
(1+R/100) = (√11236/10000)
= (√11236)/(√10000)
= 106/100
R/100 = (106/100 − 1)
=> 6/100
R = 6%
There is 80% increase in an amount in 8 years at simple interest. What will be the compound interest of Rs. 14,000 after 3 years at the same rate?
Simple interest = P * r * t /100, where, P is the Principal, r is the rate of interest and t is the time period such that the rate of interest and the time period have mutually compatible units like r % per annum and t years.
Here, in the first case, let the Principal be Rs.P and rate of interest be r % per annum. Time period is given as 8 years . Interest is given as 80 P / 100
So, 80 P / 100 = P * r * 8 / 100
Or, 80 = 8 r
So, r = 10 % per annum.
Now, in the second case, Principal is given as Rs. 14,000, rate of compound interest is 10 % per annum as determined above; and t is 3 years.
Compound interest = P * ( 1 + r/100)t - P
= 14,000 * ( 1+ 10 /100)3 - 14,000
= 14,000 * ( 1 + 0.1)3 - 14,000
= 14,000 *(1.1)3 - 14,000
(14,000 * 1.331) - 14,000
= 18,634 - 14,000 = 4,634
So, the compound interest on Rs.14,000 at the same rate of interest as in case 1 in 3 years will be Rs. 4,634.
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 is:
The difference between simple interest and compound on Rs. 900 for one year at 10% per annum reckoned half-yearly is:
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