# Quant TVM problem

An investor is evaluating an insurance product that promises to pay a \$1,000 monthly benefit for 20 years beginning 10 years from now. The investor is required to make payments at the end of each month for the next five years. Assuming a five percent discount rate and monthly compounding, the minimum monthly payment required to finance the benefit is closest to:

\$1,743

\$1,912

\$2,228

Could someone tell me their method of solving?

I did it by moving the \$1000 payment to year 30, so FV 30, and then bringing that back to time 0. Then from there computing the payments for the 5 years using the time 0 PV.

I was able to get an answer that is off by \$6, is this method correct?

Thanks

I don’t have my calculator on me, so I did this quickly in Excel. I get an exact answer of \$1,736.159, assuming all payments occur at the beginning of the month.

It doesn’t matter which date you pick as your focal date. What I did was to PV the \$1,00/month to time 10 (\$152,156.70). \$1/month for the first five years has an FV of 68.2944 t time 5; rolling that up with another 5 years’ interest produces 87.63985. 152,156.70/87.63985 = 1,736.159.

You could also just discount everything back to time 0. The answer should be identical.

Thank you so much, you’ve been very helpful. I got an answer of \$1736 as well.

1736 is based on BGN (first payment is immediate).

Your question states that the payment is at the end of each month (i.e. ordinary annuity), so you should use END in your calculator then you will get 1743.

^ In my haste, I missed that the payments in years 1-5 happen at the end of the month. Thanks for spotting that!