Statistics Problem Help

Question

Martha starts saving for her retirement by making monthly deposits into a retirement account whose annual rate is 3.7%. She plans to retire in 24 years with an amount of money that has the same buying power as $295008 has today. If the anticipated rate of inflation if 2.1%, how much should each of her deposits be?

Round your answer to the nearest dollar. 

Answer 1

I am NOT an economist so my understanding of how inflation rate influences interest rate is quite sketchy. But to answer the question I'm assuming that the inflation rate reduces the buying power of money and effectively reduces the value accrued due to interest by int%-inf%. That is, the interest rate is 3.7%/yr and the inflation rate is 2.1%/yr, so the effective annual growth rate is 3.7%-2.1% = 1.6% This is what I'll use as the growth rate r. Time period t = 24 years.

At the end of 24 years Martha wants to have S = $295,008 of today's buying power after adjusting for 24 years of inflation.

295,008 = P(1+r)^t. Find P, the total principal invested.

295,008 = P* 1.016²⁴ = P*1.46369.

Divide both sides by 1.46369 to get P = $201550.93.

Since P is the total amount invested, per month Martha should invest 201550.93/(24*12) = $699.83 or $700.00 to nearest dollar. Division is by 24*12 because there are 12 months in each of the 24 years.