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Important Formulae

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

Practice Questions

1.

 Find the interest under simple interest for a principal of ₹1200 at an interest rate of 5% per annum for a period of 4 years. A.240 B.260 C.320 D.450

I = PNR/100
Here, P = 1200
N = 4
R = 5%
I = (1200 x 4 x 5)/100 = ₹240.
I = ₹240.

2.

 What is the interest earned on ₹10,000 for 2 years at 10% per annum simple interest?(in ₹) A.2000 B.1500 C.2500 D.3000

I = PNR/100
I = (10000 x 2 x 10)/100
I = 2000.

3.

 What is the interest earned on ₹10000 for 2 years at 10% per annum compound interest, compounded annually? A.210 B.420 C.315 D.630

Interest 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 = ₹210.

4.

 If ₹2000 amount to ₹2200 in 2 years under simple interest, what is the rate of interest per annum? A.15% B.10% C.5% D.20%

I = Amount - Principal = 2200 - 2000 = ₹200.
I = PNR/100
200 = (2000 x 2 x R)/100 = 5%

5.

 If ₹20000 amount to ₹24200 in 2 years under compound interest, what is the rate of interest per annum? A.10% B.20% C.15% D.Cannot be determined

A = 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 ₹200 at 10% per annum compound interest, interest compounded every 6 months? A.₹20 B.₹20.50 C.₹25 D.₹23.20

Interest for first six months = (200 x 1/2 x 10)/100 = ₹10
Principal for next six months = 200 + 10 = ₹210
Interest for next six months = (210 x 1/2 x 10)/100 = ₹10.5
Total interest = 10 + 10.5 = ₹20.5

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

Let 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 ₹1550 is lent out into two parts, one at 8% and another one at 6%. If the total annual income is ₹106, find the money lent at each rate. A.800 B.900 C.1000 D.700

Let the sum lent at 8% be ₹ X and that at 6% be ₹ (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% = ₹650.
Money lent at 6% = ₹(1550 - 650) = ₹900.