Question

On January 1, an insurance company has 100,000 which is due to Linden as a life insurance death benefit. He chooses to receive the benefit annually over a period of 15 years, with the first payment immediately. The benefit he receives is based on an effective interest rate of 4% per annum. Every July 1, the insurance company pays 100 in expenses and taxes to maintain the policy. At the end of nine years, the company has X remaining. Calculate X.

The answer is $53,900 im just not quite sure how to get it.

Answer 1

The benefit he receives is based on an effective interest rate of 4% per annum.

The insurance company earns interest at an effective rate of 5% per annum. Every July 1, the company pays 100 in expenses and taxes to maintain the policy.

The insurance company earns interest at an effective rate of 5% per annum is the missing line in the above question. we have to caluclate 5 % interest for insurance company to get the accumulate value.

Calculate Linden's payment, P.

Calculate the accumulated value at 5% of the 100,000 after 9 years. Call that X.

Calculate the accumulated value at 5% of the payments of P after 9 years. Call that Y.

Calculate the accumulated value at 5% of the expenses of 100 9 years after the first 100 is paid. Call that Z.

Insurance company should have X - Y - Z*/(1.05)^.5

Last 1.05^.5 is because you evaluate the payments of 100 1/2 year later than the date you want for your answer

X=155132.82,

Y=100127.73 (each payment is $8648.18 by using i=4%, n1=15 yrs, then set n2=9 yrs to get Y at 5%), Z=1157.19, and

X-Y-Z/1.05^.5=53875.2

Round your answer to the nearest number that means 53,900