# TVM problem

Stephan is planning for his retirement at the age of 60, at which time he wishes to receive \$50,000 per year for 25 years. Given his current age, Stephan would want the first retirement payment to begin from year 35. For this, he plans to save \$1,000 per year for next 10 years. An appropriate discount rate for Stephan is 10%. At the end of saving period the amount still required to achieve the retirement goal will be closest to: a) \$30,140 b) \$45,540 c) \$66,950 Please help me on this question. As per my understanding the investment period will end at 45 and solved various parts of the problem as following. FV of saving @t=45; \$15,937 (PMT= -1000, N=10, I/Y=10) PV of retirement goal@t=60; \$453,852 (PMT=50,000, N=25, I/Y=10) What should be the next step from here onward?

The question is somewhat ambiguous and the way I see it is illustrated below (looks like Stephan is 25yo). None of the answers seems to fit though. (I get X=\$25,950=453852/1.10^25-15937)

X plus will lead to \$15,937 ----------------> \$453,852 |----------|----------------------------------|--------------| 25 35 60 85

In any case looks like you know how to apply the necessary inputs in TVM calculations so don’t get bogged down with the question.

P.S. Where did you find the question and isn’t there an answer available?

PV of retirement goal @ 60 should be \$499,237. Then the logic works to produce \$30,140.