For Rs 10,000 at 10% p.a. What would be the compound interest for 2 1/2 years?

Given,

Principal = Rs 10,000

R = 10% p.a

Time = 2 1/2 years

Since time is in fraction,

we use the formula

Compound interest for 2 1/2 years

= Compound interest for 2 years

+ SI for next 1/2 years

**
Compound interest for 2 years
**

Amount = P (1+R/100)^T

= 10,000 (1+10/100)^2

= 10,000 (1+1/10)^2

= 10,000 ((10 + 1)/10)^2

= 10,000 (11/10)^2

= 10,000 × 121/100

= 100 × 121

= Rs 12,100

Now,

Amount = Principal + Interest

12,100 = 10,000 + Interest

12,100 − 10,000 = Interest

2100 = Interest

Interest = Rs 2100

**
Simple interest for
**
**
1/2
**
**
years
**

Principal will be the amount after 2 years

**
P =
**
**
Rs
**
**
12100
**

R = 5% p.a

T = 1/2 years

SI = PRT/100

= (12100 × 5 × 1/2)/100

= (12100 × 5)/(100 × 2)

= (121 × 5)/2

= 605/2

= Rs 302.5

Simple interest for 1/2 years = Rs 302.5

Now,

Compound interest for 2 1/2 years

= Compound interest for 2 years

+ SI for next 1/2 years

= 2,100 + 302.5

= 2100 + 3025/1

= 24025/10

= Rs 2402.5

∴ Compound interest after 21/2 years = Rs 2402.5

#### Suppose I have Rs 1000 and I put it in a bank on compound interest. What would be the amount I have after 1 3/4 years, it interest rate is 5% pa.?

Given,

Principal = Rs 1000

Rate = 5% p.a

Time = 1 3/4 years

Since time is in fraction

We use the formula

Compound interest for 1 3/4 years

= Compound interest for 1 years

+ SI for next 3/4 years

**
Compound interest for 1 years
**

Amount = P (1+R/100)^(T,)

= 1000 (1+5/100)^1

= 1000 (1+1/20)

= 1000 ((20 + 1)/20)

= 1000 (21/20)

= 100 × 21/2

= 50 × 21

= Rs 1050

Now,

Amount = Principal + Interest

1050 = 1000 + Interest

1050 − 1000 = Interest

50 = Interest

Interest = Rs 50

**
Simple interest for
**
**
3
**
**
/
**
**
4
**
**
years
**

Principal will be the amount after 1 year

**
P =
**
**
Rs
**
**
1050
**

R = 5% p.a

T = 3/4 years

S.I = PRT/100

= (1050 × 5 × 3/4)/100

= (1050 × 5 × 3)/(100 × 4)

= (105 × 5 × 3)/(10 × 4)

= (21 × 5 × 3)/(2 × 4)

= 315/8

= Rs 39.375

Now,

Interest after 1 3/4 years = Compound interest for 1 year

+ Simple interest for next 3/4 year

= 50 + 39.375

= Rs 89.375