2. Jenn lends Joe $24,000 at a nominal annual interest rate of 18%, compounded m

Question

2. Jenn lends Joe $24,000 at a nominal annual interest rate of 18%, compounded monthly. Joe is to repay the loan by making monthly payments over the course of two years starting one month after the loan was made. Find the amount of payment, interest, principal repayment, and outstanding balance for Joe's 13th payment in each of the following cases (a) Joe repays the loan by making interest-only payments, and a lump sum payment of prin- cipal at the end. (b) Joe makes level payments of principal (plus interest accrued) (c) Joe makes equal monthly payments.

Explanation / Answer

a)

interest per month = 24000 * 18%/12 = 360

monthly payment = 360

lump sum amount = 24000

for 13th payment

amount of payment = 360

interest = 360

principal = 0

outstanding balance = 24000

b)

princial replayment = 24000/24 = 1000

outstanding balance = 24000 - 12000 = 12000

interest = 12000 * 18%/12 = 180

monthly payment = 1000 + 180 = 1180

c)

x * [1-(1+18%/12)^-24]/18%/12 = 24000

monthly payment x = 1198.18

amount paid = 1198.18 * [1-(1+18%/12)^-12]/18%/12 = 13069.16

outstanding principal = 24000 -13069.16 = 10930.84

interest = 196.04

principal = 1002.14

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