Question

Prepare an amortization schedule for a five-year loan of $84,000. The interest rate is 8% per year and the loan calls for equal annual payments. How much interest is paid in the third year? How much total interest is paid over the life of the loan?

Provide another amortization schedule if you must pay $8,400 toward the principle each year instead of equal annual payments. How much interest is paid in the third year? Explain why the third year interest paid in the case of equal payment is different from when you must to pay $8,400 toward the principle every year.  

Answer 1

Part A:

Instalment = Loan / PVAF (r%, n)

PVAF (r%, n) = Sum [ PVF(r%, n) ]

PVF (r%, n) = 1/1 (1+r)^n

r - Int Rarte per anum

n - No. of Years

Instalment = Loan / PVAF (r%, n)

= $84,000 / PVAF (8%,5)

= $84,000 / 3.9927

= 21038.34

Loan Amortization Schedule:

Year	Opening Bal	Instalment	Int	Principal	Closing Bal
1	$ 84,000.00	$ 21,038.34	$ 6,720.00	$ 14,318.34	$ 69,681.66
2	$ 69,681.66	$ 21,038.34	$ 5,574.53	$ 15,463.81	$ 54,217.85
3	$ 54,217.85	$ 21,038.34	$ 4,337.43	$ 16,700.91	$ 37,516.93
4	$ 37,516.93	$ 21,038.34	$ 3,001.35	$ 18,036.99	$ 19,479.95
5	$ 19,479.95	$ 21,038.34	$ 1,558.40	$ 19,479.95	$         -0.00

Int Paid in Year 3 = $ 4,337.43

Tota Int Paid = [No. of Instalments * INstalment ] - Principal

= [ 5 * 21038.34 ] - 84000

= 105191.71 - 84000

= 21191.71

Part B:

Year	Opening Bal	Principal Repay	Int	Instalment	Closing Bal
1	$ 84,000.00	$ 8,400.00	$         6,720.00	$ 15,120.00	$ 75,600.00
2	$ 75,600.00	$ 8,400.00	$         6,048.00	$ 14,448.00	$ 67,200.00
3	$ 67,200.00	$ 8,400.00	$         5,376.00	$ 13,776.00	$ 58,800.00
4	$ 58,800.00	$ 8,400.00	$         4,704.00	$ 13,104.00	$ 50,400.00
5	$ 50,400.00	$ 8,400.00	$         4,032.00	$ 12,432.00	$ 42,000.00
6	$ 42,000.00	$ 8,400.00	$         3,360.00	$ 11,760.00	$ 33,600.00
7	$ 33,600.00	$ 8,400.00	$         2,688.00	$ 11,088.00	$ 25,200.00
8	$ 25,200.00	$ 8,400.00	$         2,016.00	$ 10,416.00	$ 16,800.00
9	$ 16,800.00	$ 8,400.00	$         1,344.00	$   9,744.00	$   8,400.00
10	$   8,400.00	$ 8,400.00	$            672.00	$   9,072.00	$               -

Int paid for Year 3 is = $ 5376

In earlier case Opening Bal on Year 3 is $ 54,217.85 & present opening bal for Year 3 is $ 67,200.00

Thus there is inc in Int amount for year 3 as there is inc in Opening Bal.

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