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# A sum of Rs 550 was taken as a loan.This is to be paid back in two equal installments.If the rate of interest be 20% compounded annually, the the amount of each installment will be?

Asked by Priyanshu 15th March 2013, 6:09 PM
I1=interest paid in the first payment
I2=interest paid in the second payment
P1=principal paid in the first payment
P2=principal paid in the second payment

Because the payments are equal:
I1 + P1 = I2 + P2

Because all the principal is paid:
P1 + P2 = 550

First payment interest is on the full loan:
I1 = 550 x 0.2x 1 = 110 (Using simple interest itself as the interest rate is compounded anually, so the interest computed for any first year will be same as that computed using the simple interest.

Second payment interest is only on the remaining principal:
I2 = (550-P1) x 0.2 x1

Substituting:
110 + P1 = (550 - P1)(0.2) + (550-P1)
110 + P1 = 110 - 0.2P1 + 550 - P1
2.2P1 = 550
P1 = 250
Hence, each Payment = P1+ I1 = 250 + 110 = Rs. 360
Answered by Expert 16th March 2013, 5:27 AM
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