Question

A 30 year loan of $100, 000 is taken out at effective annual interest i = 4%. For the first 20 years you pay 130% of interest, while for the last 10 years you pay constant payments X. Find X.

Answer 1

The Future value of the loan at the end of 30 years will be= 100,000*(1.04)^30 = 324,339.75.

Paying 130% of the interest in the initial 20 years means that 30% more interest has been paid which will reduce the principal amount.The interest for 20 years will be = 20*0.04*100,000 = 80,000. 30% of this amount will be = 24,000. Hence, the principal now becomes 76,000. This amount has to be converted to 10 annuity installments. Let it be X.

X/1.04 + X/1.04^2 + .......+X/1.04^10 = 76,000.

X = 9370.112