Question

a)Maria wants to buy a car. She has saved $2,500 for a down payment, and she can afford payments of $250 per month for 5 years. Her credit union has offered her an auto loan that charges 4.8% per year compounded monthly for 5 years. What is the largest loan she can afford? What is the most expensive car she can afford?

b) Find the interest rate needed for an investment of $5100 to triple in 6 years if interest is compounded continuously

Answer 1

a) Down payment = $2,500

n = 5 * 12 = 60 monthly payments

r = 4.8%/12 = 0.004

Largest loan Maria can offord is $13,312.21695625

The most expensive car she can afford = Loan amount + Down payment

The most expensive car she can afford = 13,312.21695625 + 2,500

The most expensive car she can afford = $15,812.21695625

b) r = ln(FV/PV)/n

FV = 15,300

PV = 5,100

n = 6

r = ln(15,300/5,100)/6

r = ln(3)/6

r = 1.0986122887/6

r = 0.1831020481

r = 18.31020481%

Interest rate needed is 18.31020481%