Question

7. Loans and Financing: a. Ken and Marcy plan to have their kitchen remodeled at a cost of $6,000. The carpenter suggests that they pay $600 down, followed by 18 monthly payments of $325. What is the finance charge for this payment schedule?

b. Trevor asks his bank for a loan of $22,000 to add a guest room to his house. His bank offers financing at 7.25% compounded monthly, for a term of 5 years, payable monthly. What is Trevor’s monthly payment?

N = I% = PV = PMT = FV = P/Y = C/Y = PMT: END BEGIN

c. Kawai requires a loan of $33,000 to buy a used sport utility vehicle. His banks offers financing at 6.75% compounded monthly, for a term of 6 years, payable monthly. What is the total cost of this loan?

N = I% = PV = PMT = FV = P/Y = C/Y = PMT: END BEGIN N = I% = PV = PMT = FV = P/Y = C/Y = PMT: END BEGIN

d. Huan accepted an in-store loan on a computer she just purchased. The monthly payment is $64.53 on the $2,000 computer with a 12% APR for 3 years. Determine the portion of the monthly payment that will go towards interest and principal for the first two months.

Answer 1

a]

finance charge = total amount paid - cost of kitchen

total amount paid = down payment + (monthly payment * total number of payments)

total amount paid = $600 + ($325 * 18) = $6,450

finance charge = $6,450 - $6,000

finance charge = $450

b]

I/Y = 7.25 (annual rate of interest)

N = 5 (number of years)

PV = 22000 (loan amount)

FV = 0 (loan balance outstanding at end of 5 years is zero)

P/Y = 12 (12 monthly payments per year)

C/Y = 12 (monthly compounding)

PMT: END (each payment is at month-end)

CPT --> PMT

PMT is calculated to be $438.23

Monthly payment is $438.23

c]

I/Y = 6.75 (annual rate of interest)

N = 6 (number of years)

PV = 33000 (loan amount)

FV = 0 (loan balance outstanding at end of 5 years is zero)

P/Y = 12 (12 monthly payments per year)

C/Y = 12 (monthly compounding)

PMT: END (each payment is at month-end)

CPT --> PMT

PMT is calculated to be $558.66

Monthly payment is $558.66

Total cost of loan = (monthly payment * total number of payments) - loan amount

Total cost of loan = ($558.66 * (6 * 12)) - $33,000

Total cost of loan = $7,223.81

d]

Month 1

Interest = loan outstanding at beginning of month * APR / 12 = $2,000 * 12% / 12 = $20

Principal = monthly payment - interest = $64.53 - $20 = $44.53

loan outstanding at end of month = loan outstanding at beginning of month - principal payment

loan outstanding at end of month = $2,000 - $44.53 = $1,955.47

Month 2

loan outstanding at beginning of month = loan outstanding at end of previous month  = $1,955.47

Interest = loan outstanding at beginning of month * APR / 12 = $1,955.47 * 12% / 12 = $19.55

Principal = monthly payment - interest = $64.53 - $19.55 = $44.98