Question

ross has decided that he wants to build enough retirement wealth that, if invested at 6 percent per year, will provide him with $2,500 monthly income for 30 years. to date, he has saved nothing, but he still has 20 years until he retires. how much money does he need to contribute per month to reach his goal?

Answer 1

Step-by-step explanation:

To calculate the amount Ross needs to contribute per month to reach his retirement goal, we can use the concept of present value and the formula for the present value of an ordinary annuity.

Given:

Interest rate (r) = 6% per year = 0.06 (in decimal form)

Monthly income goal (PMT) = $2,500

Number of years in retirement (n) = 30

Number of years until retirement (t) = 20

We want to find the present value (PV) of the future stream of monthly income that Ross desires. The formula for the present value of an ordinary annuity is:

PV = PMT * [(1 - (1 + r)^(-n)) / r]

Substituting the given values:

PV = $2,500 * [(1 - (1 + 0.06)^(-30)) / 0.06]

Using a financial calculator or spreadsheet software, the present value (PV) is approximately $343,642.91.

Now, we need to determine the monthly contribution (PMT_contribution) Ross needs to make for the next 20 years to accumulate this amount. The formula for the future value of an ordinary annuity can be rearranged to solve for the payment amount:

PMT_contribution = PV / [((1 + r)^t - 1) / r]

PMT_contribution = $343,642.91 / [((1 + 0.06)^20 - 1) / 0.06]

Using a financial calculator or spreadsheet software, the monthly contribution (PMT_contribution) is approximately $233.07.

Therefore, Ross needs to contribute approximately $233.07 per month for the next 20 years to reach his retirement goal of $2,500 monthly income for 30 years, assuming a 6% annual interest rate.