## Aptitude Simple And Compound InterestPage 1

Principal:

The money borrowed or lent out for a certain period is called the principal or the sum.

Interest:

Extra money paid for using other's money is called interest.

Simple Interest (S.I.):

If the interest on a sum borrowed for certain period is reckoned uniformly, then it is called simple interest.
Let Principal = P, Rate = R% per annum (p.a.) and Time = T years.
Then,
Simple Interest (SI) = P x R x T/100

Compound Interest (C.I.)

Let Principal = P, Rate = R% per annum, Time = n years

When interest is compound Annually:
Amount = P(1+R/100)n

When interest is compounded Half-yearly:
Amount = P[1+(R/2)/100]2n

When interest is compounded Quarterly:
Amount = P[1+(R/4)/100]4n

1.

 Find the interest under simple interest for a principal of â‚¹1200 at an interest rate of 5% per annum for a period of 4 years. (a)240 (b)260 (c)320 (d)450
Here, P = 1200
N = 4
Â R = 5%
I = (1200 x 4 x 5)/100 = â‚¹240.
I = â‚¹240.

2.

 What is the interest earned on â‚¹10,000 for 2 years at 10% per annum simple interest?(in â‚¹) (a)2000 (b)1500 (c)2500 (d)3000
I = (10000 x 2 x 10)/100
I = 2000.

3.

 What is the interest earned on â‚¹10000 for 2 years at 10% per annum compound interest, compounded annually? (a)210 (b)420 (c)315 (d)630
Answer is: AInterest for the first year
= (1000 x 1 x 10)/100 = 100
Principal for second year
= 1000 + 100 = 1100
Interest for the second year = (1100 x 1 x 10)/100 = 110
Hence, Total interest for the two years = 100 + 110 = â‚¹210.

4.

 If â‚¹2000 amount to â‚¹2200 in 2 years under simple interest, what is the rate of interest per annum? (a)15% (b)10% (c)5% (d)20%
Answer is: CI = Amount - Principal = 2200 - 2000 = â‚¹200.
I = PNR/100
200 = (2000 x 2 x R)/100 = 5%

5.

 If â‚¹20000 amount to â‚¹24200 in 2 years under compound interest, what is the rate of interest per annum? (a)10% (b)20% (c)15% (d)Cannot be determined
Answer is: AA = P(1 + R/100)^N
24200 = 20000(1 + R/100)^2
1.21 = (1 + R/100)^2
R = 10%

6.

 What is the interest earned in the first year on â‚¹200 at 10% per annum compound interest, interest compounded every 6 months? (a)â‚¹20 (b)â‚¹20.50 (c)â‚¹25 (d)â‚¹23.20
Answer is: BInterest for first six months = (200 x 1/2 x 10)/100 = â‚¹10
Principal for next six months = 200 + 10 = â‚¹210
Interest for next six months = (210 x 1/2 x 10)/100 = â‚¹10.5
Total interest = 10 + 10.5 = â‚¹20.5

7.

 At what rate percent per annum will a sum of money double in 16 years? (a)6 (b)13/2 (c)25/4 (d)31/5
Answer is: CLet principal = P.
Then, S.I. = P
And T = 16 years.
R = (100 x P)/(P x 16)% = 25/4% p.a.

8.

 A sum of â‚¹1550 is lent out into two parts, one at 8% and another one at 6%. If the total annual income is â‚¹106, find the money lent at each rate. (a)800 (b)900 (c)1000 (d)700
Answer is: BLet the sum lent at 8% be â‚¹ X and that at 6% be â‚¹ (1550 - X).
[8 x 1 x X]/100 + [(1550 - X) x 6 x 1]/100 = 106
8X + 9300 - 6X = 10600
2X = 1300
X = 650
Money lent at 8% = â‚¹650.
Money lent at 6% = â‚¹(1550 - 650) = â‚¹900.