Question

For the cash in flows and out flows shown, what will the payment have to be at the end of Year 8 to pay off the loan taken on Year 0. The rate of interest is as shown and is a yearly rate with annual compounding.

	RATE	6%
Years	Cash in flows	Cash out flows
0	$650,000
1		($100,000)
2		($125,000)
3		($150,000)
4		($175,000)
5		$0
6		($200,000)
7		$0
8		???

Group of answer choices

$61,936

$11,785

$6,302

$54,077

Answer 1

The payment is computed as shown below:

Year 0 cash inflow = Year 1 cash flow / ( 1 + required rate of return )¹ + Year 2 cash flow / ( 1 + required rate of return )² + Year 3 cash flow / ( 1 + required rate of return )³ + Year 4 cash flow / ( 1 + required rate of return )⁴ + Year 5 cash flow / ( 1 + required rate of return )⁵ + Year 6 cash flow / ( 1 + required rate of return )⁶ + Year 7 cash flow / ( 1 + required rate of return )⁷ + Year 8 cash flow / ( 1 + required rate of return )⁸

$ 650,000 = $ 100,000 / 1.06¹ +  $ 125,000 / 1.06² +  $ 150,000 / 1.06³ +  $ 175,000 / 1.06⁴ +  $ 0 / 1.06⁵ +  $ 200,000 / 1.06⁶ +  $ 0 / 1.06⁷ + Value of cash flow in year 8 / 1.06⁸

$ 650,000 - $ 611,140.57 = Value of cash flow in year 8 / 1.06⁸

$ 38,859.43 x 1.06⁸ = Value of cash flow in year 8

Value of cash flow in year 8 = $ 61,936 Approximately

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