Question

How much should you deposit at the end of each month in an IRA that pays 13% compounded monthly to earn $50,000 per year from interest alone, while

leaving the principal untouched, to be withdrawn at the end of each year after you retire in 30 years?
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The monthly deposit is $
(Round up to the nearest dollar)

Answer 1

To calculate the monthly deposit needed to earn $50,000 per year in interest alone, we can use the present value of an annuity formula:

PV = PMT x ((1 - (1 + r/n)^(-nt)) / (r/n))

Where PV is the present value, PMT is the monthly deposit, r is the annual interest rate (13%), n is the number of times the interest is compounded per year (12), and t is the number of years (30).

We want to solve for PMT, so we can rearrange the formula:

PMT = PV / ((1 - (1 + r/n)^(-nt)) / (r/n))

Since we want to earn $50,000 per year in interest alone, and the principal will be untouched, the present value is $0. So the formula simplifies to:

PMT = ($50,000 / ((1 - (1 + 0.13/12)^(-12*30)) / (0.13/12)))

Using a financial calculator or spreadsheet, we can calculate that the monthly deposit needed is approximately $436.

Therefore, to earn $50,000 per year in interest alone, while leaving the principal untouched, you would need to deposit approximately $436 at the end of each month into an IRA that pays 13% compounded monthly, for a period of 30 years.