Question

Joe secured a loan of $13,000 four years ago from a bank for use toward his college expenses. The bank charges interest at the rate of 5%/year compounded monthly on his loan. Now that he has graduated from college, Joe wishes to repay the loan by amortizing it through monthly payments over 15 years at the same interest rate. Find the size of the monthly payments he will be required to make. (Round your answer to the nearest cent.)
$

10.

The price of a new car is $12,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 6%/year compounded monthly. (Round your answers to the nearest cent.)(a) What monthly payment will she be required to make if the car is financed over a period of 48 months? Over a period of 72 months?

48 months	$
72 months	$

(b) What will the interest charges be if she elects the 48-month plan? The 72-month plan?

48-month plan	$
72-month plan	$

Answer 1

9. Loan Value 4 years ago =13000
Number of months =4*12 =48
Rate per month =5%/12
Value of loan today =Loan Value 4 years ago*(1+r)^n =13000*(1+5%/12)^48 =15871.6396
Number of months of payment =15*12 =180
Size of Monthly Payment =Value of loan today /((1-(1+r)^-n)/r) =15871.6396/(((1-(1+5%/12)^-180)/(5%/12))=125.51

10. PV of loan amount =Value of Car*(1-Down Payment)=12000*(1-25%)=9000
Rate per month =6%/12 =0.5%
a) Monthly payment  if the car is financed over a period of 48 months =PV/((1-(1+r)^-n)/r) =9000/((1-(1+0.5%)^-48)/0.5%)=211.37
Monthly payment  if the car is financed over a period of 72 months =PV/((1-(1+r)^-n)/r) =9000/((1-(1+0.5%)^-72)/0.5%)=149.16

b)Interest  if she elects the 48-month plan =PMT*48-PV =211.37*48-9000=1145.53
Interest  if she elects the 72-month plan =PMT*72-PV =149.16*72-9000=1739.23