Actuarial Outpost FM Problem Help
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

 Financial Mathematics Old FM Forum

#1
06-11-2019, 10:49 PM
 Siny Member SOA Join Date: Aug 2018 College: University of California, Riverside Posts: 30
FM Problem Help

Hi again!

I am having trouble with the following problem:

At time t=0, Paul deposits P into a fund crediting interest at an effective annual interest rate of 8%. At the end of each year in years 6 through 20, Paul withdraws an amount sufficient to purchase an annuity-due of 100 per month for 10 years at a nominal interest rate of 12% compounded monthly. Immediately after the withdrawl at the end of year 20, the fund value is zero. Calculate P.

The solution states: a double-dot angle 120 at .01 multiplied by 100 = \$7,039.75

I get everything except for the "multiplied by 100" part.

The problem says "100 per month"

Originally, I converted the 100 to per year: 100 x 12 = 1200. Why did they multiply 100 instead of 1200? Why didn't they change it to "per year" since we have to convert nominal interest rate to annual interest rate?
#2
06-11-2019, 10:56 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,305

Quote:
 Originally Posted by Siny Hi again! I am having trouble with the following problem: At time t=0, Paul deposits P into a fund crediting interest at an effective annual interest rate of 8%. At the end of each year in years 6 through 20, Paul withdraws an amount sufficient to purchase an annuity-due of 100 per month for 10 years at a nominal interest rate of 12% compounded monthly. Immediately after the withdrawl at the end of year 20, the fund value is zero. Calculate P. The solution states: a double-dot angle 120 at .01 multiplied by 100 = \$7,039.75 I get everything except for the "multiplied by 100" part. The problem says "100 per month" Originally, I converted the 100 to per year: 100 x 12 = 1200. Why did they multiply 100 instead of 1200? Why didn't they change it to "per year" since we have to convert nominal interest rate to annual interest rate?
They could have treated it as a 10 year annuity, multiplying by 1200. It should give the same answer as a 120 month annuity of 100.

You say “we have to convert nominal interest rate to annual interest rate”, but you don’t need an annual interest rate. They used 1% per month, which is fine. There are often multiple valid ways to do an FM problem.