Question

An insurance company is offering a new policy to its customers. Typically the policy is bought by a parent or a grandparent for a child at the child's birth. The details of the policy are as follows: The purchaser(say, the parent) makes the following six payments to the insurance company:

First birthday: $400

Second birthday: $500

Third birthday: $600

Fourth birthday: $700

Fifth birthday: $800

Sixth birthday: $900

After the child's sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $250,000. If the relevant interest rate is 11 percent for the first six years and 7 percent for all subsequent years, is the policy worth buying?

Answer 1

First we calculate present value of payments made to insurance company and payments received from insurance company.
If present value of Payment received from insurace company is more than payments made to insurance company, then policy is worth buying.
Otherwise, not.
Interest rate for six years =				11%
Interest rate for subsequent years =				7%
Present value of payments made to Insurance company
Year	Cash Outflow	P.V.F. @ 11%	Present value
1	400	0.900901	$360.36
2	500	0.811622	$405.81
3	600	0.731191	$438.71
4	700	0.658731	$461.11
5	800	0.593451	$474.76
6	900	0.534641	$481.18
	Total		$2,621.94
Present value of payments received by insurance company
Future value =	250000
I =	7%
n =	65
Present value = Future value / (1+i)^n
	250000 / (1+0.07)^65
	$3,076.06
Decision : Present value of payments received by insurance company is $3076.06 more than payments made to insurance company ($2621.94)
So, Policy is worth buying.