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: $ 760
Second birthday: $ 760
Third birthday: $ 860
Fourth birthday: $ 850
Fifth birthday: $ 960
Sixth birthday: $ 950
After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $260,000. The relevant interest rate is 10 percent for the first six years and 7 percent for all subsequent years.
Find the future value of the payments at the child's 65th birthday: Future Value $____________
Answer:
We need to find the FV of the premiums to compare with the cash payment promised at age 65. We have to find the value of the premiums at year 6 first since the interest rate changes at that time. So: |
FV1 = $760(1.10)5 = $1,223.99 |
FV2 = $760(1.10)4 = $1,112.72 |
FV3 = $860(1.10)3 = $1,144.66 |
FV4 = $850(1.10)2 = $1,028.50 |
FV5 = $960(1.10)1 = $1,056.00 |
Value at Year 6 = $1,223.99 + 1,112.72 + 1,144.66 + 1,028.50 + 1,056.00 + 950 |
Value at Year 6 = $6,515.87 |
Finding the FV of this lump sum at the child’s 65th birthday: |
Future Value = $6,515.87(1.07)59 = $352,870.55. The policy is not worth buying; the future value of the deposits is $352,870.55, but the policy contract will pay off $260,000. The premiums are worth $92,870.55 more than the policy payoff. |
An insurance company is offering a new policy to its customers. Typically, the policy is bought...
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