Question

Your neighbour makes you the following offer. He would like to borrow $24,000 today. He will repay this amount by making 23 annual payments with the first payment being made at the end of this year. If the payments grow by 13.50% each year and the appropriate discount rate is 16.50%, how much will your neighbour pay you at the end of the first year?

Question 17 options:

$1,596

$1,636

$1,676

$1,716

$1,756

Answer 1

	Present value of Growing annuity =	P/(r - g) × [ 1 - [(1+g)/(1+r)]n ]
P=	Periodic payment	$                               1,596
g=	Growth rate	13.50%
r=	Rate of interest per period:
	Annual rate of interest	16.50000%
	Frequency of payment	once in every 12 months
	Payments per year	12/ 12=	1
	Interest rate per period	0.165/1=	16.500%
n=	number of payments:
	Number of years	23
	Payments per year	1
	number of payments	23
	Present value of annuity=	1596/(0.165 - 0.135) × [ 1 - [(1+ 0.135)/(1 + 0.165 )]^23 ]
	Present value of annuity=	24,004.21

Answer is 1,596

At this first payment present value of payments equal to $24,000

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