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

First birthday: $920
Second birthday:920
Third birthday: 1020
Fourth birthday: 1020
Fifth birthday: 1,120
Sixth birthday: 1,120

After the child's sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $430,000. The relevant interest rate is 12 percent for the first 6 years and 7 percent for all subsequent years. What is the value of the policy at the child's 65th birthday?

Answer 1

Value at the end of 6 years
= 1120 + 1120(1.12) + 1020(1.12)^2 + 1020(1.12)^3 + 920(1.12)^4 + 920(1.12)^5
= 8155.91

now the rate goes down to 7% for the next
59 years.
Final value at age 65
= 8155.91(1.07)^59
= 441,687.52

but they only paid out $430,000
while using that money to invest in other business ventures. Mmmmh, can you see why "insurance" is a profitable business to be in?

Answer 2

Hi Reiny,

I came up with the same answer using the same logic you did. Unfortunately, I am doing this question through an online system that checks my answer automatically, and the system says that the answer is wrong. I have tried every variation that I can think of, and still can't come up with the right answer. :( Any other ideas?

Answer 3

Never mind!!! It helps to put the answer to the correct question! :)