4.37 A well-known insurance company offers a policy known as the “Estate Creator
ID: 2744251 • Letter: 4
Question
4.37 A well-known insurance company offers a policy known as the “Estate Creator Six Pay.” Typically, a parent or grandparent buys a policy 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 $750 Fourth Birthday $800 Second Birthday $750 Fifth Birthday $800 Third Birthday $750 Sixth Birthday $800 No more payments are made after the child’s sixth birthday. When the child reaches the age of 65, he or she receives $250,000. If the relevant interest rate is six percent for the first six years and seven percent for all subsequent years, is the policy worth buying?
Explanation / Answer
Calculation of Future value of Present “Estate Creator Six Pay” policy:
Year
Cash flows
Future value factor @ 6%
Future value
cash flow
1
$ 750
1.000000
$ 750.00
2
$ 750
1.060000
$ 795.00
3
$ 750
1.123600
$ 842.70
4
$ 800
1.191016
$ 952.81
5
$ 800
1.262477
$ 1,009.98
6
$ 800
1.338226
$ 1,070.58
6th Year end
$ 5,421.07
FV = PV at the end of 6th year × (FVIFA, i= 7%, n = 59)
= $5,421.07 × 74.5533
= $404,160 (rounded to nearest $10)
The future value should be $404,160 but he receives only $250,000 at the age of 65 years of the child. Therefore, it is not advisable to buy this policy as it is not worth.
Year
Cash flows
Future value factor @ 6%
Future value
cash flow
1
$ 750
1.000000
$ 750.00
2
$ 750
1.060000
$ 795.00
3
$ 750
1.123600
$ 842.70
4
$ 800
1.191016
$ 952.81
5
$ 800
1.262477
$ 1,009.98
6
$ 800
1.338226
$ 1,070.58
6th Year end
$ 5,421.07
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