Q
What annual payment will discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest. (S.S.C. 2000)
The total amount is Rs. 1936.
The rate of interest is 14%.
The time is 4 years.
The type of installment is annual.
Concept:
In simple all installments are always the same if no conditions apply.
Simple interest is the one where interest once credited does not earn interest on it.
Formula used:
Instalment = (100 × Amount)/{(100 × t) + (r × t × ((t – 1)/2))}
Where T is time and R is the rate of interest.
Calculation:
The total amount is Rs. 1936.
The rate of interest is 14%.
The time is 4 years.
Then we calculate the first installment by using formula
⇒ Instalment = (100 × Amount)/{(100 × t) + (r × t × (t – 1)/2))}
⇒ Installment = (100 × 1936)/{(100 × 4) + (14 × 4 × ((4 – 1)/2))}
⇒ Installment = 193600/(400 + 84)
⇒ Installment = 193600/484 = Rs. 400
Thus, the annual payment will be Rs. 400.
Alternate Method
Let the first installment be Rs. 100
Now the total installment is 4.
Now to find the next installment we add the rate of interest in the previous installment every time.
Then second installment
⇒ 100 + 14 = Rs. 114
Third installment = 114 + 14 = Rs. 128
Fourth installment = 128 + 14 = Rs. 142
Total amount
⇒ 100 + 114 + 128 + 142 = Rs. 484
∵ when amount is Rs. 484 then first installment is 100
∴ if the amount is Rs. 1936 then installment
⇒ (100/484) × 1936 = Rs. 400.
Thus, the annual payment will be Rs. 400.