You need $17,000 to purchase a used car. Your wealthy uncle is willing to lend y
ID: 2742231 • Letter: Y
Question
You need $17,000 to purchase a used car. Your wealthy uncle is willing to lend you the money as an amortized loan. He would like you to make annual payments for 5 years, with the first payment to be made one year from today. He requires a 9% annual return.
What will be your annual loan payments? Round your answer to the nearest cent. Do not round intermediate calculations.
How much of your first payment will be applied to interest and to principal repayment? Round your answer to the nearest cent. Do not round intermediate calculations.
Interest: $
Principal repayment: $
Explanation / Answer
Sol) Calculation of annual loan payments. Payments to annually for 5 years and required a 9% annual return. Amount of loan is $17,000. so we calculate the annual payments to be made
PMT = {PV+[PV+FV/(1+i)^N-1]}i
where pv= present value of the amount of loan PMT= annual payments to be made i= annual return
n = no of periods.
PMT = {$17,000+[$17,000+$0/(1+0.09)^5-1]}0.09
= {$17,000+[$17,000+$0/0.5386]}0.09
={$17,000+$31,536.3123}0.09
= $4,370.70
Annual loan payments is $4,370.70
B) First payment will be applied to interest and to principal repayment.
$14,159.30.
Calculation of interest $17,000*0.09 =$1,530
Calculation of principal amount = $4,370.70-$1,530=$2,840.70
Period Begnining balance Payment Interest component Principal component Ending balance 1 $17,000 $4,370.70 1530 $2,840.70$14,159.30.
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