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**

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