Jennifer has a deposit of $5,000,000 at St. George bank. Effective annual interest rate is 15%. Jennifer wants to withdraw a series of consecutive payments at the end of each year that continue indefinitely, and each payment grows at 3%. Calculate the value of the first withdrawal at the end of year 1.

Question

BlackTom AI · Accepted Answer

We start by identifying the structure of the cash flow and the relevant formulas.
The deposit is the present value of an infinite series of end-of-year withdrawals that grow by a fixed rate each year. For a growing perpetuity with initial payment X at the end of year 1 and growth rate g, discounted at the effective annual rate i, the present value at time 0 is X / (i - g) provided i > g.
Here, i = 0.15 (15%), g = 0.03 (3%), and the present value (the deposit) is 5,000,000. 
Set up the equation: 5,000,000 = X / (0.15 - 0.03) = X / 0.12.
Solve for X: X = 5,000,000 × 0.12 = 600,000.
Thus, the value of the first withdrawal at the end of year 1 should be 600,000.

Now evaluate the given options:
Option 1: $750,000.00
If the first payment were 750,000, the present value would be 750,000 / 0.12 = 6,250,000, which exceeds the 5,000,000 deposit. Therefore this cannot be correct.

Option 2: $600,000.00
This yields a present value of 600,000 / 0.12 = 5,000,000, which matches the deposit exactly. This is consistent with the growth rate and interest rate given.

Option 3: $743,552.40
PV would be 743,552.40 / 0.12 ≈ 6,196,270, far above the 5,000,000 deposit. This option overstates the initial withdrawal.

Option 4: $855,085.26
PV would be 855,085.26 / 0.12 ≈ 7,125,711, again well above 5,000,000. This also overstates the initial payment.

In summary, the correct approach is to equate the present value of the growing perpetuity to the deposit and solve for the first payment. The only option whose PV matches 5,000,000 is $600,000.00, while the other options imply larger PVs and are therefore incorrect.

25400 Financial Literacy - Spring 2025 🔴 Practice Questions for In-class Quiz 1

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