A man has to discharge a debt of ₹15,600 which is due in 3 years at 4% simple interest per annum. If he pays this amount in equal instalments of annual payment, find the amount for annual payment.
- A₹5,200
- B₹5,100
- C₹5,400
- D₹5,000
Solution & Step-by-step Explanation
Let the annual installment be ₹x.
The total amount due at the end of 3 years is ₹15,600.
The first installment is paid at the end of the 1st year, so it accumulates interest for (3−1)=2 years.
The second installment is paid at the end of the 2nd year, so it accumulates interest for (3−2)=1 year.
The third installment is paid at the end of the 3rd year, so it accumulates no interest.
The sum of all these values equals the total debt:
(x+
100
x×4×2
)+(x+
100
x×4×1
)+x=15600
(x+
100
8x
)+(x+
100
4x
)+x=15600
3x+
100
12x
=15600
100
312x
=15600
312x=1560000
x=
312
1560000
=5000
Thus, the annual payment is ₹5,000.
The total amount due at the end of 3 years is ₹15,600.
The first installment is paid at the end of the 1st year, so it accumulates interest for (3−1)=2 years.
The second installment is paid at the end of the 2nd year, so it accumulates interest for (3−2)=1 year.
The third installment is paid at the end of the 3rd year, so it accumulates no interest.
The sum of all these values equals the total debt:
(x+
100
x×4×2
)+(x+
100
x×4×1
)+x=15600
(x+
100
8x
)+(x+
100
4x
)+x=15600
3x+
100
12x
=15600
100
312x
=15600
312x=1560000
x=
312
1560000
=5000
Thus, the annual payment is ₹5,000.