Question

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 is 20% p.A. Compound interest, being compounded annually, then the value of each installment is:

Answer 1

Answer:

Step-by-step explanation:

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