Question

Derek decides to buy a new car. The dealership offers him a choice of paying $515.00 per month for 5 years (with the first payment due next month) or paying some amount today. He can borrow money from his bank to buy the car. The bank requires a 5.00% interest rate. What is the most that he would be willing to pay today rather than making the payments?

Derek plans to buy a $28,418.00 car. The dealership offers zero percent financing for 58.00 months with the first payment due at signing (today). Derek would be willing to pay for the car in full today if the dealership offers him $____ cash back. He can borrow money from his bank at an interest rate of 4.48%.

Suppose you deposit $1,037.00 into an account 5.00 years from today that earns 10.00%. It will be worth $1,609.00 _____ years from today.

Please round answers to 2 decimal places. :)

Answer 1

Answer 1)

Present Value Annuity =

where r is the rate of Return for compounding period = 5% / 12 = 0.00416666666

n is the no of compounding period 5 years * 12 = 60

=

= 27290.21

Answer 2)

monthly payment at 0% Financing = 28418 / 58 months = 489.97

Present Value =

r = 4.48% / 12 = 0.00373333333

n = 58 months

=

= 25604.68

Therefore, a cash back of 28418 - 25604.68 = $2813.32 will make derek Pay today.

Answer 3)

Future Value = present value * (1+r)^n

1609 = 1037 * (1+0.10)^n

(1+0.10)^n = 1609 / 1037

(1+0.10)^n = 1.55159112825

logging both sides

n * log 1.10 = log 1.55159112825

n * 0.04139268515 = 0.1907772877

n = 0.1907772877 / 0.04139268515

n = 4.61

No of years from today = 4.61 + 5 = 9.61 years