Question

A person purchases a house with a loan from a bank for a value $2,500,000 to be paid monthly (uniform series) during 5 years at a rate of 1.25% monthly interest. After making 12 monthly payments, this person decides to pay off the debt in one final payment in month 13. How much would he have to pay to the bank to finish off the debt?

Answer 1

t = 5*12 = 60 months

Monthly payment = 2500000 * (A/P,1.25%,60)

= 2500000 * 0.0125*((1 + 0.0125)^60)/((1 + 0.0125)^60-1)

= 2500000 * 0.0125*((1.0125)^60)/((1.0125)^60-1)

= 2500000*0.023789930

= 59474.83

Principal amount due after making 12 payments = 59474.83 * (P/A,1.25%,48)

= 59474.83 *((1 + 0.0125)^48-1)/(0.0125*(1 + 0.0125)^48)

= 59474.83 *((1.0125)^48-1)/(0.0125*(1.0125)^48)

= 59474.83 *35.931481

= 2137018.55

Amount due at 13th payment = 2137018.55 * 1.0125 = 2163731.28