Question

I really need help with these two questions! Please help, thank you!!!

1. Derek plans to buy a $31,030.00 car. The dealership offers zero percent financing for 56.00 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 4.35%.

2. Suppose you deposit $1,029.00 into an account 6.00 years from today that earns 12.00%. It will be worth $1,940.00 _____ years from today.

Answer 1

1.) When Derek takes a loan for the amount of $ 31,030, bank charges a rate of interest of 4.35% annually. So for 56 installments, payment of which begins today, Derek would have to pay $ 611.036 as EMI.

If we multiply the same amount with 56 and subtract it with the offer price of the car today, Derek will be willing to pay the amount in full.

EMI of the loan from the bank = $ 611.036

Total amount in EMI = $ 611.036 * 56 = $ 34,218.

Cash back required = $ 34,218.00 - $ 31,030.00 = $ 3,188.00 (Answer)

2.) Amount Deposited(PV) = $ 1029.00

Amount required(FV) = $ 1940.00

Rate of interest (r) = 12%

Solving for n( using trial and error method or using financial calculator)

n = 5.6 years.

Since the money was deposited 6 years ago,  it's already worth $ 1940.00.

(5.6 - 6) years = 0.4 years ago. (Ans)