On September 1, 2018, Susan Chao bought a motorcycle for $32,000. She paid $1,200 down and...

On September 1, 2018, Susan Chao bought a motorcycle for $32,000. She paid $1,200 down and financed the balance with a five-year loan at an annual percentage rate of 7.4 percent compounded monthly. She started the monthly payments exactly one month after the purchase (i.e., October 1, 2018). Two years later, at the end of October 2020, 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, 2020? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Expert Solution

EMI = [P x R x (1+R)^N]/[(1+R)^N-1]
Where,
EMI= Equal Monthly Payment
P= Loan Amount =32000-1200 =30800
R= Interest rate per period =7.4%/12 =0.6166667%
N= Number of periods =12*5 =60

= [ $30800x0.0061666667 x (1+0.0061666667)^60]/[(1+0.0061666667)^60 -1]

= [ $189.93333436( 1.0061666667 )^60] / [(1.0061666667 )^60 -1

=$615.71
Calcualtion of loan outstnading after 2 years
Present Value Of An Annuity
= C*[1-(1+i)^-n]/i]

Where,
C= Cash Flow per period
i = interest rate per period
n=number of period

= $615.706[ 1-(1+0.006166667)^-36 /0.006166667]

= $615.71[ 1-(1.006166667)^-36 /0.006166667]

= $615.71[ (0.1985) ] /0.006166667

= $19,822.93





Amount to be paid = $19822*1.01

=$20021.16

jeff jeffy answered 2 years ago

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