Mike Polanski is 30 years of age and his salary next year will be $40,000. Mike forecasts that his salary will increase at a steady rate of 5% per annum until his retirement at age 60. a. If the discount rate is 8%, what is the PV of these future salary payments? b. If Mike saves 5% of his salary each year and invests these savings at an interest rate of 8%, how much will he have saved by age 60? c.If Mike plans to spend these savings in even amounts over the subsequent 20 years, how much can he spend each year?

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zainsubhani zainsubhani · Answer 1 · 2020-02-11T09:49:14+01:00

Answer:

Part A:

[tex]PV=\$760662.5271[/tex]

Part B:

Money saved by age 60:

[tex]FV=\$382714.3014[/tex]

Part C:

Money spend each year:

[tex]C=\$38980.29695[/tex]

Explanation:

Part A:

The formula for Growing Annuity is given by:

[tex]PV=C[\frac{1}{r-g}-\frac{1}{r-g}(\frac{(1+g)^T}{(1+r)^T)}][/tex]

Where:

r is discount rate

g is increase per annum

T is time

C is salary

[tex]PV=\$40,000[\frac{1}{0.08-0.05}-\frac{1}{0.08-0.05}(\frac{(1+0.05)^{30}}{(1+0.08)^{30}})]\\PV=\$760662.5271[/tex]

Part B:

PV of salaries*0.05=$38033.1264 (PV calculated in Part A)

FV(Money Saved)=[tex]PV(1+r)^T[/tex]

[tex]PV(1+r)^t\\FV=\$38033.1264(1+0.08)^{30}\\FV=\$382714.3014[/tex]

Part C:

[tex]PV=C[\frac{1}{r}-\frac{1}{r*(1+r)^t}][/tex]

Where

C is savings spend each year

r is the interest Rate

t is time= 20 years

PV as FV calculated in Part B

[tex]\$382714.3014=C[\frac{1}{0.08}-\frac{1}{0.08-(1+0.08)^2^0}]\\C=\$38980.29695[/tex]