Q:

A certain college graduate borrows 5510 dollars to buy a car. The lender charges interest at an annual rate of 17%. Assuming that interest is compounded continuously and that the borrower makes payments continuously at a constant annual rate k dollars per year, determine the payment rate that is required to pay off the loan in 7 years. Also determine how much interest is paid during the 7-year period. Round your answers to two decimal places. Payment rate dollars per year Interest paid dollars Click if you would like to Show Work for this question: Open Show Work SHOW HINT UNK TO TEXT

Accepted Solution

A:
Answer:His annual payment rate required to pay off the loan in 7 years is [tex]k = $2362.41[/tex] a year.He has to pay $11026.85 in interestStep-by-step explanation:The first step to solve this problem is find how much the student will have to pay for the car. So, we have to find how much the present value of the car(in $) will be worth in 7 years. This is a compound interest problem:The compound interest formula is given by:[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.In this exercise, we have:A = The value we want to findP = The initial value = 5510r = 0.17n = 1t = 7So[tex]A = 5510(1 + \frac{0.17}{1})^{7}[/tex][tex]A = $16536.85[/tex]In a seven year period, he has to pay $16536.85. Per year, he has to pay a rate k of:[tex]k = \frac{16536.85}{7} = $2362.41[/tex]His annual payment rate required to pay off the loan in 7 years is [tex]k = $2362.41[/tex] How much does he pay in interest?His loan is $5510 and he has to pay $16536.85. So, in interest, he has to pay [tex]16536.85 - 5510 = $11026.85[/tex]