Question

The terms of a single parent's will indicate that a child will receive an ordinary annuity of $10,000 per year from age 18 to age 24 (so that the child can attend college) and that the balance of the estate goes to a niece. If the parent dies on the child's 10th birthday, how much money must be removed from the estate to purchase the annuity? (Assume an interest rate of 7%, compounded annually. Round your answer to the nearest cent.)

Answer 1

Amount Required at 18 Years:

PV of future CFs required.

Year	CF	PVF @7%	Disc CF
18	$ 10,000.00	1.0000	$ 10,000.00
19	$ 10,000.00	0.9346	$   9,345.79
20	$ 10,000.00	0.8734	$   8,734.39
21	$ 10,000.00	0.8163	$   8,162.98
22	$ 10,000.00	0.7629	$   7,628.95
23	$ 10,000.00	0.7130	$   7,129.86
24	$ 10,000.00	0.6663	$   6,663.42
Value Required at 18 Years			$57,665.40

FV of Annuity :

Let X be the Annuity

Year	CF	FVF @7%	FV of CF
11	X	1.6058	1.6057X
12	X	1.5007	1.5007X
13	X	1.4026	1.4025X
14	X	1.3108	1.3107X
15	X	1.2250	1.2250X
16	X	1.1449	1.1449X
17	X	1.0700	1.07X
18	X	1.0000	1X
FV of Annuity			10.2598X

FV of Annuity = 57665.40

This 10.2598X = 57665.40

X = 57665.4 / 10.2598

= $ 5620.52

Pls comment, if any further assistance is requoired.