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issacnewton
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Homework Statement
Mike Polanski is 30 years of age and his salary next year will be $40000. Mike forecasts that his salary will increase at a steady rate of 5% per annum until his retirement at age 60.
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 ?
Problem is from Principles of Corporate Finance (10 edition) by Brealey, Myers, Allen
Homework Equations
Annuity equation, Compound interest equation
The Attempt at a Solution
Here is my attempt at a solution. Mike is saving 5% of his salary. At the end of first year, he will get $40000. So he will save $2000 at the end of the first year. Now let ##r=0.08## and let ##g = 0.05##. So in the first year, Mike saves $2000. Now in the second year, the salary becomes ##40000(1+g)##. Mike saves ##40000g = 2000## out of this. So in the second year, Mike will save $2000 again. So saving each of the 30 years is $2000. So we have a saving cash flow of $2000 for 30 years. I will now calculate the present value of this annuity and then use the compound interest formula to get the future value. Now 30 year annuity factor is $$\mbox{AF} = \frac{1}{r}\left[1-\frac{1}{(1+r)^{30}}\right] = 11.25778$$ So the present value of the savings cash flow is $$\mbox{PV} = 2000 \times \mbox{AF} = 22515.57$$ We want to find out how much is the savings when Mike is 60 years old. So we can now just use the compound interest formula to forward this value. So future value of this is $$\mbox{FV} = 22515.57 (1+r)^{30} = 226566.4$$ So Mike will save $226,566.40 when he is 60. But the correct answer given is $382,714.30. So I don't know where I have gone wrong. Please help.
Thanx