A sum of rupees 9600 is invested for 3 years at 10% p.a. compound interest
Answers
Solution!!
The concept of compound interest has to be used here. The principal, time and rate of interest is given in the question. We will find the compound interest and the amount with and without the formula.
Principal = Rs 9600
Time = 3 years
Rate of interest = 10%
Amount = P(1 + (R/100))ⁿ
Amount = 9600(1 + (10/100))³
Amount = 9600(110/100)³
Amount = 9600(11/10)³
Amount = 9600 × (1331/1000)
Amount = Rs 12777.6
CI = Amount - Principal
CI = Rs 12777.6 - Rs 9600
CI = Rs 3177.6
Now let's do it without the formula.
First year:-
Principal = Rs 9600
Rate of interest = 10%
Time = 1 year
SI = (P × R × T)/100
SI = (9600 × 10 × 1)/100
SI = 96 × 10 × 1
SI = Rs 960
Amount = Principal + SI
Amount = Rs 9600 + Rs 960
Amount = Rs 10560
Second year:-
The amount in the first year becomes the principal in the second year.
Principal = Rs 10560
Rate of interest = 10%
Time = 1 year
SI = (P × R × T)/100
SI = (10560 × 10 × 1)/100
SI = 1056 × 1 × 1
SI = Rs 1056
Amount = Principal + SI
Amount = Rs 10560 + Rs 1056
Amount = Rs 11616
Third year:-
The amount in the second year becomes the principal in the third year.
Principal = Rs 11616
Rate of interest = 10%
Time = 1 year
SI = (P × R × T)/100
SI = (11616 × 10 × 1)/100
SI = 116160/100
SI = Rs 1161.6
Amount = Principal + SI
Amount = Rs 11616 + Rs 1161.6
Amount = Rs 12777.6
CI = Amount in third year - Principal in first year
CI = Rs 12777.6 - Rs 9600
CI = Rs 3177.6
Abbreviations used:-
P → Principal
T and n → Time
R → Rate of interest
SI → Simple interest
CI → Compound interest