Final answer:
To have the ability to withdraw $53,750 each year for 15 years with a 3% interest rate, you would need approximately $643,043.79 in your account at the beginning. Over the 15-year period, you will take out approximately $806,250 from the account. The interest earned on the account during this time is approximately -$163,206.21.
Step-by-step explanation:
In order to find out how much money you need to have in your account at the beginning, you can use the formula for the present value of an annuity:
PV = PMT × [(1 - (1 + r)-n)) / r]
Where PV is the present value, PMT is the annual withdrawal amount, r is the interest rate per period, and n is the number of periods. Plugging in the given values into the formula, we can calculate the present value:
PV = $53,750 × [(1 - (1 + 0.03)-15)) / 0.03] ≈ $643,043.79
So, you would need approximately $643,043.79 in your account at the beginning.
To calculate the total amount of money you will take out of the account over 15 years, you can multiply the annual withdrawal amount by the number of years:
Total money taken out = $53,750 × 15 = $806,250
Therefore, you will take out approximately $806,250 from the account over 15 years.
To find out the amount of interest earned, you subtract the total amount of money taken out from the total account balance:
Interest earned = Total account balance - Total money taken out = $643,043.79 - $806,250 = -$163,206.21
Thus, the amount of interest earned is approximately -$163,206.21.