Question

1. Let's take a specific example. Assume you borrow Bo = $15,000 with a fixed annual interest rate of 6%, or 0.5% per month. As a first problem, assume that your monthly payment is $500. The goal is to compute the number of months required to pay off the loan. Every month, two things happen: Interest, which is 0.5% of the current balance, is added to the current balance and the loan balance is decreased by the monthly payment of $500. We let Bn be the loan balance after the nth payment. Explain why B1 = Bo + 0.005B0 – 500 = 1.005B0 – 500.

Answer 1

Solution Given, Loan amount (B) = $15,000 Rate of interest (8) = 6 7 yearly = 0.5% monthly Monthly payment (MPA) = $500 We know that, Bor Monthly payment 5oo 15000 * 0.5 .5/100 n 1-14 0.5 loo 17 100 100 २० 100.5 or - In (1009/005) 32.58 33 8 x Bo So, no. of beriod (n)= 33 months Again, after first payment, Interest = 0.005 Bo Monthly payment Principal = Bot 0.005 Bo Rest Loan (B) = principal a payment And, 500 So 3 Boto.005 Bot 500 B. 1.005 Bo-500 = $1 4 575