Don\'t Use Excel An insurance company has made you the following retirement offe

Question

Don't Use Excel

An insurance company has made you the following retirement offer. If you pay them $100,000 now, you will receive payments of $8000 a year for 10 years. After this they will pay you $9000 a year forever. Recall that a “Capitalized Cost” is the amount of money that will provide annual payments indefinitely by paying out the interest.
a)   What is the Capitalized Cost of the $9,000 payments in terms of variable (i) at Year 10?

b)   Solve for the rate of return (i) for the overall investment to the nearest 0.5%

Explanation / Answer

As per the statement in the question 100000=8000/(1+R)^1+8000/(1+R)^2+8000/(1+R)^3+8000/(1+R)^4+8000/(1+R)^5+8000/(1+R)^6+8000/(1+R)^7+8000/(1+R)^8+8000/(1+R)^9+8000/(1+R)^10+9000/(R*(1+R)^10) By solving we get R=9.5%=Rate of return Capitalized Cost of the $9,000 payments in terms of variable (i) at Year 10=9000/(0.095)=94736.84

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