# Arithmetic Aptitude :: Compound Interest

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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?

ARs. 51.25

BRs. 54.25

CRs. 60

DRs. 52

Explanation:

Sum = Rs. (50 * 100)/(5*2) = Rs. 500.

Amount = Rs. [500 * (1 + 5/100)2]

= Rs. (500 * 21/20 * 21/20 )
= Rs. 551.25

C.I. = Rs. (551.25 - 500) = Rs. 51.25

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What is the difference between the compound interests on Rs. 5000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?

ARs. 2.04

BRs. 3.06

CRs. 4.80

DRs. 8.30

Explanation:

C.I. when interest

compounded yearly=rs.[5000*(1 4/100)(1 1/2*4/100)]

= Rs. 5304.

C.I. when interest is

compounded half-yearly=rs.5000(1 2/100)^3

= Rs. 5306.04

Difference = Rs. (5306.04 - 5304) = Rs. 2.04

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A sum of money amounts to Rs.6690 after 3 years and to Rs.10035 after 6 years on compound interest. Find the sum.

ARs.4400

BRs.4560

CRs.4600

DRs.4460

Explanation:

Let's assume the Sum = Rs. P.
P [1 + (R/100)]^3 = 6690 -------- (i)
P [1 + (R/100)]^6 = 10035 ----------(ii)
On dividing, we get [1 + (R/100)]^3 = 10035/6690 = 3/2.
P * (3/2) = 6690 or P = 4460.
Hence, the sum is Rs. 4460.

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The difference between the compound interest and the simple interest on a certain sum at 12% p.a. for two years is Rs.90. What will be the value of the amount at the end of 3 years?

A9780.8

B8780.80.

C7654.4

DNone of these

Explanation:

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A sum of money doubles itself at C.I. in 15 years. In how many years will it become eight times?

A40 years.

B35 years.

C55 years.

D45 years.

Explanation:

P [1 + (R/100)]^15 = 2P => [1 + (R/100)]^15 = 2 ----------- (i)
Let P [1 + (R/100)]^n = 8P => P [1 + (R/100)]^n = 8 = 2^3
= [{1 + (R/100)}^15]^3.
=> [1 + (R/100)]^n = [1 + (R/100)]^45.
=> n = 45.
So, the required time = 45 years.

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The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?

ARs. 3406

BRs. 4096

CRs. 3096

DRs. 4085

Explanation:

Formula: P = Amount / (1 + R/100)^n
Principal = [4913 / (1 + 25/(4 * 100))3]
=> 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096

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Anil invests an amount for 2 years at the rate of 15% per annum at simple interest.Had he invested in a scheme in which interest was compounded yearly he would have got Rs.450 more. Find the principal:

ARs.8,000

BRs.15,000

CRs.20,000

DRs.10,000

Explanation:

Lets assume D amount difference between compound and simple interest for 2 years, D=P*(R/100)^2
where P is the principal
R is rate of interest

so here,
450 = P*(15/100)^2 => P= Rs. 20000

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If the compound interest (compounded Yearly) on a certain sum for 2 years at 3% is Rs.101.50 then what will be the corresponding simple interest?

ARs.98.25

BRs.100.00

CRs.90.00

DRs.95.50

Explanation:

Given, years = 2
3% of 50= (50*(3/100))=Rs.1.5
Simple Interest =50+50=100
Compound Interest=50+50+1.5=101.5

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If the compound interest on a sum of Rs.5000 at the rate of 10% per annum is Rs.1050, then time period is (Interest compounded yearly):

A1 Years

B21/2 Years

C3 Years

D2 Years

Explanation:

C.I of 5000 at 10% interest for x years is 6050 = Rs. 1050
6050 = 5000 ( 1 + 10/100)^n => 6050/5000 = (11/10)^n
=> 605/500 = (11/10)^n => n = 2 years.

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At what rate of interest (compounded yearly)will Rs. 10,000 amount to Rs. 12,100 in 2 years?

A9%

B11%

C8%

D10%

Explanation:

Amount = P(1 + R/100)^n
Where Principal = P, Rate = R% per annum, Time = n years.
12100 = 10000 (1+R/100)^2
=> 121/100 = (1+R/100)^2
=> 11/10 = (1+R/100)=> 11/10 = (100 + R)/100
=> 110 = 100 + R => R = 10%

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