Question

11. Mike plans to make contributions to his retirement account for 15 years. After the last contribution, he will start withdrawing $10,000 a quarter for 10 years. Assuming Mike's account earns 8% compounded quarterly, how large must his quarterly contributions be during the first 15 years, in order to accomplish his goal?

Answer 1

To solve this problem, we need to use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A = future value of the account

P = present value (the contributions)

r = interest rate (as a decimal)

n = number of times the interest is compounded per year

t = number of years

First, we need to find the future value of the account (A) after 10 years of withdrawals at $10,000 per quarter. This means there will be 40 quarters in total ($10,000 * 40 = $400,000).

Next, we need to find the present value of the account (P) after 15 years of contributions.

Let's call the quarterly contributions "x".

We can set up the equation as follows:

$400,000 = x * (1 + 0.08/4)^(4 * 15) - $10,000 * (1 + 0.08/4)^(4 * 10)

We can now solve for x using a financial calculator or by using a programming language to perform the calculation. The result of this calculation is that Mike's quarterly contributions should be $2,597.29 in order to accomplish his goal.