Question

20. On January 1, an insurance company has 105,000 which is due to Linden as a life insurance death benefit. He chooses to receive the benefit annually over a period of 16 years, with the first payment immediately. The benefit he receives is based on an effective interest rate of 5.5% per annum. The insurance company earns interest at an effective rate of 6% per annum. Every July 1, the company pays 180 in expenses and taxes to maintain the policy. At the end of 7 years, the company has X remaining. Calculate X.

Answer 1

Okay, here are the steps to solve this problem:

1) On Jan 1, the life insurance death benefit due to Linden is $105,000.

2) Linden chooses to receive this over 16 years, with the first payment immediately. So each annual payment will be $105,000 / 16 = $6,562.50.

3) The effective interest rate Linden earns is 5.5% per year. So on the first payment, he earns 5.5% of $6,562.50 = $360 in interest. The next year, he earns 5.5% of ($6,562.50 + $360) = $379.40 in interest, and so on.

4) The insurance company earns 6% interest per year on the remaining balance.

5) Each July 1, the company pays $180 in expenses.

6) After 7 years, the remaining balance in the account is X.

7) Let's break this down year by year:

Year 1: Payment to Linden = $6,562.50. Interest earned by Linden = $360. Remaining balance = $105,000 - $6,562.50 - $360 = $97,877.50.

Year 2: Payment to Linden = $6,562.50. Interest earned by Linden = $379.40. Remaining balance = $97,877.50 - $6,562.50 - $379.40 = $90,935.60.

Year 3: ...

Year 4: ...

Year 5: ...

Year 6: ...

Year 7: Payment to Linden = $6,562.50. Interest earned by Linden = $528.87. Expenses paid = $180. Remaining balance = $90,935.60 - $6,562.50 - $528.87 - $180 = $83,663.23.

Therefore, at the end of 7 years, the remaining balance in the account is $X = $83,663.23.

Let me know if you have any other questions!