Professor Lucas retired from teaching at his university at age 65. He is to receive a pension from the university.In addition to that, he will get $2,500 at the end each month for 25 years at 6% compounded monthly. This payment comes from his personal Retirement Savings Plan, which has a balance of $526,308.21 in it. His monthly payments are indexed for inflation at a fixed rate. What is the inflation rate at which his monthly payments are indexed? Can this be solved for the information given? I don't even know where to start. Any help or hint would be greatly appreciated. I thank you.
Yes, it certainly CAN be solved!!. It is not really that much different from an ordinary annuity. The only slight difficulty is separating the investment rate of 6% from the "indexing" rate, which are blended together. But we know how to do that. Will use this common TVM formula:
PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}=2,500=526,308.21.R.{[ 1 + R]^300 / [ 1 + R ]^300 - 1}, solve for R, which is the blended interest rate. Plugging these number into my computer, which is programmed to solve TVM problems of this type, gives a blended rate of 2.9925% monthly compound. We divide this by 1200=.00249375 blended monthly rate. Since we know the investment rate is 6% comp. monthly, then the monthly rate is 6/1200=.005. Or, 1.005, which we will divide by the blended monthly rate we got above, 1.00249375 thus: 1.005 / 1.00249375=1.0025 -1 =.0025 x 100 =.25%. This is the monthly index rate of his annuity payments. Or, .25 x 12=3% compounded monthly. And that is it.
Good luck to you.
