Question

Jane would like to retire on $15,000 per month with the first retirement check on the day she retires. She expects to live for 30 years after retirement. If her investment account earns 9%, how much must she have in the account on the day she retires to fund this retirement? (could you please show formulas)

a. 5,400,000

b. 407,004

c. 2,180,000

d. 1,878,210

e. 1,864,228

Answer 1

The amount is computed as shown below:

Present value = Monthly amount x [ (1 – 1 / (1 + r)ⁿ) / r ] x (1 + r)

r is computed as follows:

= 9% / 12 (Since the payments are on monthly basis, hence divided by 12)

= 0.75% or 0.0075

n is computed as follows:

= 30 year x 12 months (Since the payments are on monthly basis, hence multiplied by 12)

= 360

So, the amount is computed as follows:

= $ 15,000 x [ (1 - 1 / (1 + 0.0075)³⁶⁰ ) / 0.0075 ] x 1.0075

= $ 15,000 x 124.2818657 x 1.0075

= $ 1,878,210 Approximately

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