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:

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: $800
Second birthday:800
Third birthday: 900
Fourth birthday: 900
Fifth birthday: 1,000
Sixth birthday: 1,000

After the child's sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $350,000. The relevant interest rate is 11 percent for the first 6 years and 7 percent for all subsequent years, is the policy worth buying?

Answer 1

To determine if the policy is worth buying, we need to calculate the present value of the payments made by the purchaser and compare it with the future value of $350,000 received by the child at age 65.

To calculate the present value (PV) of the payments, we will discount each payment at the relevant interest rate for that period. The relevant interest rate for the first 6 years is 11 percent, and for all subsequent years, it is 7 percent.

Let's calculate the present value of the payments:

First birthday: PV = $800 / (1 + 0.11)^1 = $800 / 1.11 = $720.72
Second birthday: PV = $800 / (1 + 0.11)^2 = $800 / 1.2321 = $649.74
Third birthday: PV = $900 / (1 + 0.11)^3 = $900 / 1.36393 = $659.40
Fourth birthday: PV = $900 / (1 + 0.11)^4 = $900 / 1.51163 = $595.27
Fifth birthday: PV = $1,000 / (1 + 0.11)^5 = $1,000 / 1.6681 = $599.40
Sixth birthday: PV = $1,000 / (1 + 0.11)^6 = $1,000 / 1.8477 = $541.24

Now, let's calculate the present value of all the payments:

PV of payments = $720.72 + $649.74 + $659.40 + $595.27 + $599.40 + $541.24
= $3,765.77

Next, we need to calculate the future value (FV) of $350,000 received by the child at age 65. We will discount this future value back to the present using the relevant interest rate of 7 percent.

FV = $350,000 / (1 + 0.07)^65 = $350,000 / 16.9657055 = $20,612.64

Now, we can compare the present value of the payments ($3,765.77) with the present value of the future value ($20,612.64).

If the present value of the payments is less than the present value of the future value, then the policy is worth buying. If it is the other way around, then it may not be worth buying.

In this case, since $3,765.77 < $20,612.64, the policy is worth buying.