Question

phan wants to withdraw $2,500 at the beginning of each year for the next five years. he wants to have $10,000 left at the end of the five years. phan expects to earn 5% compounded annually on his investment. what lump sum should he deposit today?

Answer 1

Phan needs to calculate the present value of both the annual withdrawals and the final sum he desires using the formulas for present value of an annuity and the present value of a lump sum. Combining these values will give him the initial deposit required to fulfill his financial goals, considering a 5% annual compound interest rate.

Step-by-step explanation:

To calculate the lump sum Phan needs to deposit today, we must consider both the withdrawals of $2,500 at the beginning of each year and the final $10,000 he wants left after five years, with a 5% compound annual interest rate.

The future value of an annuity formula to calculate the withdrawals is: PV = PMT × [(1 - (1 + r)^-n)/r], where PMT is the annual withdrawal amount, r is the annual interest rate, and n is the number of periods.

The present value of the $10,000 that Phan desires to have at the end of five years is calculated using the formula: PV = FV / (1 + r)^n.

Combining both calculations gives us the total amount Phan needs to deposit today. By substituting values, we can then solve for the present value.

In this case, the computation is a bit more complex due to combining an annuity and a single value, which can be solved using financial calculators or spreadsheet software.