A debt of $6000 due four years from now and $6000 due nine years from now...

Question

Question

A debt of $6000 due four years from now and $6000 due nine years from now is to be repaid by a payment of $2100 in one year,

Answer 1

Answer #1

We know that Present value of the Future Cash outfllows is equal to the loan amount

So the total present value of the loan amount as on today = $ 6000+$ 6000= $ 12000

Hence PV of the future cash outflows is equal to the $ 12000

Let the Cash outflow in Year 5 is X

Year	Cash outflow	Disc @ 2.1%	Discounting factor	Discounted Cash flow( Cash outflow* Discounting factor)
1	$2,100	1/( 1.021)^1	0.9794	$2,056.81
2	$0	1/( 1.021)^2	0.9593	$0.00
3	$4,200	1/( 1.021)^3	0.9396	$3,946.14
4	$0	1/( 1.021)^4	0.9202	$0.00
5	X	1/( 1.021)^5	0.9013	0.9013X
	Total			$12,000

Writing it in the form of equation

$ 2056.81+$ 0+$ 3946.14+$ 0+$0.9013X = $ 12000

$ 6002.94+ 0.9013X = $ 12000

0.9013X = $ 12000-$ 6002.94

0.9013X = 5997.06

X = $ 5997.06/0.9013

X = $ 6653.789

Hence the Cash flow is 5th year is $ 6653.79 .

The final payment should be $ 6653.79.

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Answer 2

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