Question

Question 8 (of 10) value: 1.00 points On September 1. 2013, Susan Chao bought a motorcycle for $40,000. She paid S1,100 down and financed the balance with a five-year loan at an APR of 8.2 percent, compounded monthly. She started the monthly payments exactly one month after the purchase (ie., October 1, 2013). Two years later, at the end of October 2015, Susan got a new job and decided to pay off the loan. If the bank charges her a 1 percent prepayment penalty based on the loan balance, how much must she pay the bank on November 1, 2015? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Total payment References eBook & Resources Worksheet Section: 4.5 Loan Amortization Difficulty: 3 Challenge Check my work

Answer 1

Given,

Motorcycle price = $ 40000

Down payment = $ 1100

APR = 8.2%

Monthly rate (r) = 8.2%/12 = 0.683333% or 0.00683333

Term = 5 years

Term in months (n) = 5 years x 12 months = 60

Prepayment penalty = 1% or 0.01

Solution :-

Let monthly payments be "C"

Amount boowed Down Payment = Motor cycle Price %3D $40000 $38900 $1100 Now, Amount borrowed - 38900= 60 (1+0.00683333) 0.0068.3333 38900 (1,00683333) 0,00683333 38900 x 0.00683333 = 1. So47177R c0.s047/772 L1.50471772 265.816537 =

1.50471772 0.5047/772 265.816537 %3D $792.48 So, 7१२.५४ The amount remauining o the loan is Jhe present Value of the incining payments. Since, the fixst made on October1,2013 was poyment Cind made on Octobeol, She a pay ment there 2015, are 35 payments gemain- -ing, with the first payment due immediately. So, we can find the value of the remauining 34 present payments (November 1, 201s to August, 2018) and add the payment made

this date, He rg n= 34 payments. Now, (1+8)" 7१२. ५४ 0.00 683333 34 (1+0,00683333 792.48 0.00 683333 34 (1.00683333) 7१२. ५४ %3D 0.00683333 1.260543545 792.48 0.00683333 0.260543545 1.360543545 $23970.57 is the PU of 34 demaining This payments.

Now, Tortal Payment - PU ot 34 paymext(1+ Paepayment penality) + Current Payment due on November 1, 2015 $23970. S7 (+ 0.01) + $792.48 $23970.57/1.01) + $792.48 %3D २५२।०. २१९7 + छ 7१२.५8 $25002.76 Total payment = $2500R.76 Thus,