Question

An insurance company is offering a new policy to its customers. Typically, the policy is bought by a parent or 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: $ 940 Second birthday: $ 940 Third birthday: $ 1,040 Fourth birthday: $ 1,040 Fifth birthday: $ 1,140 Sixth birthday: $ 1,140 After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $130,000. If the relevant interest rate is 9 percent for the first six years and 5 percent for all subsequent years, what is the value of the policy at the child's 65th birthday

Answer 1

Answer:

The value of the policy assuming the proposed rates is 142,769.63

Explanation:

Time line:

<--/--/--/--/--/--/----------------------------------------------------------//-->

We have 6 payment and then, a lump sum capitalize until age 65

First we calculatethe value up to the end of the six year:

$Principal \: (1+ r)^{time} = Amount$

First year:

$940 \: (1+ 0.09)^{6} = Amount$

Amount 1,576.47

Second year:

$940 \: (1+ 0.09)^{5} = Amount$

Amount 1,446.31

Third Year:

$1040 \: (1+ 0.09)^{4} = Amount$

Amount 1,468.04

Fourth year:

$1040 \: (1+ 0.09)^{3} = Amount$

Amount 1,346.83

Fifth year:

$1140 \: (1+ 0.09)^{2} = Amount$

Amount 1,354.43

Six year:

$1140 \: (1+ 0.09)^{1} = Amount$

Amount 1,242.60

Sum at the end of the six year: 7,080.25‬

Then this capitalize up to 65 birthday:

from the seventh birthday up to the 65th birthday

65 - 7 = 58 years

$Principal \: (1+ r)^{time} = Amount$

Principal 8,426.68

time 58.00

rate 0.05000

$8426.68 \: (1+ 0.05)^{58} = Amount$

Amount 142,769.63