14) (10 points) You finance a brand new Mazerati by agreeing to make monthly pay

Question

14) (10 points) You finance a brand new Mazerati by agreeing to make monthly payments over a 5-yr period. The purchase price is S150,000 and the annual rate is 2.4% compounded monthly. The monthly payment is given below for your convenience. Complete the amortization table for the first two periods (no work needed):PMT $2655.50 Unpaid Payment Payment Principal Balance Interest 0 N/A NIA NIA $150,000 5.50 $2655.5 15) (5pts) For the car above, how much total interest will you pay over the 5 years. Round to the nearest dollar amount

Explanation / Answer

14. The completed table is as under:

Payment

Payment ($)

Interest ($)

Principal

Unpaid balance

0

N/A

N/A

N/A

$ 150000

1

2655.50

300

147344.50

$147644.50

2

2655.50

295.29

144689.00

$ 145284.29

It is assumed that the payment starts from the end of the 1st month and since the interest is being compounded monthly, hence interest is charged on the entire unpaid balance including interest.

However, if the payment starts at the beginning of the 1st month, the table would be as under:

Payment

Payment ($)

Interest ($)

Principal

Unpaid balance

0

N/A

N/A

N/A

$ 150000

1

2655.50

294.69

147344.50

$147639.19

2

2655.50

289.97

144689.00

$ 145273.66

It is assumed that the interest is being charged on the entire unpaid balance including interest.

15. If payments are made at the beginning of each period, then , after n payments, the outstanding balance B = A (1+r)n- p/r[(1+r)n-1] where A is the amount of loan, r is the rate of interest per period, and p is the payment per period. Here, A = $150000, n = 60, r = 0.024/12 = 0.002 and p = $ 2655.5. Then, B = 150000(1+0.002)60 –(2655.5/0.002)* [ (1+0.002)60 -1] = 150000(1.002)60 -1327750[(1.002)60-1] = 150000*1.12736174 -1327750* [1.12736174-1] = 169104.26-169104.26 = 0

Payment

Payment ($)

Interest ($)

Principal

Unpaid balance

0

N/A

N/A

N/A

$ 150000

1

2655.50

300

147344.50

$147644.50

2

2655.50

295.29

144689.00

$ 145284.29

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