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Let's do this by taking an example
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
= Rs 2402.5
∴ Compound interest after 2 1/2 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
