Question

Gabriel Lombardo just retired today. He is going to take out a withdrawal of $150,000 today to fund his quest for extreme sports for 3 years. Then he will make 30 annual unequal withdrawals from his savings with the first withdrawal occurring at t=2. He wants each withdrawal to have the same purchasing power as $70,000 has today so the withdrawals need to grow at a constant rate of 3% to compensate for expected inflation per year. His savings account earns 9% per year. How much needs to be in his savings account today in order for him to be able to withdraw $150,000 today and make 30 additional withdrawals (from t=2 through t=31)? Round all calculations to the nearest dollar.

Please solve using TI-84!

a. $1,125,232

b. $1,259,406

c. $1,077,781

d. $1,143,928

e. $777,781

Answer #1

**Hence, the correct answer is the third option i.e.
option c. $1,077,781**

We need to find the PV of growing annuities at the end of year 1. PV of growing annuitie is given by

In your TI-84, enter:

P = PMT = 70,000 escalated by two years = 70,000 x (1 +
g)^{2} = 70,000 x (1 + 3%)^{2} = 74,263.00

r = 9%

g = 3%

n = 30

PV = ???

You should get PV as = 1,011,281.93

This is the PV at the end of year 1.

Hence, amount required in his savings account today = C0 + PV / (1 + r) = 150,000 + 1,011,281.93 / (1 + 9%) = 1,077,781.59

**Hence, the correct answer is the third option i.e.
option c. $1,077,781**

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