You obtain a loan of $7500 at 16.5% compounded monthly. If you make $300 payments monthly, what is the term of the loan? Find the size of the concluding payment if: a. the last full payment is increased to pay off the loan b. the last smaller payment is made one month after the last full payment.

last installment is $540

Step-by-step explanation:

principal amount (p) = $7500

rate (r) = 16.5 %

installment = $300

to find out

full payment is increased to pay off the loan and the last smaller payment is made one month after the last full payment

solution

we know monthly installment is $300 so amount will be paid i. e.

amount = $300*12*N ... 1

here N is no of installment

and we know amount formula i. e.

amount = principal (1+r/100) ^N

put amount value and principal rate

300*12*N = 7500 (1+16.5/100) ^N

(3600 * N) / 7500 = 1.165^N

0.48N = 1.165^N

by the graphical we will get N = 3.65

so 3.65 year

so as that put N in equation 1 we get

amount = $300*12 * 3.65

amount = $13140

we can say there are 43 installment so remaining money is $13140 - ($300 * 43 installment)

i. e. = $240 and last installment will be $300 + $240 = $540

so last installment is $540