So there are two KU engineers, Tom and Mary, who decide to marry. Being good eng

Question

So there are two KU engineers, Tom and Mary, who decide to marry. Being good engineers, they have a "plan" for life. They want to retire in good style.. .early in life. They each make $ 85,000 per year. They figure they can live on Mary's salary alone for 5 years, then will need half of Tom's salary as well. They will invest Tom's full salary at 10% per year for the first 5 years and then half his salary for the duration. They think they can retire when they accumulate 3 million $. 1. They are currently both 21 years old. When can they retire? Round up to nearest whole year. (Thát way you don't have to interpolate.) a. b. If they anticipate a $ 5,000 per year pay raise every year, how much additional money would they have at that retirement age. (use the rounded number of years) (Hint.. its more than you think!)

Explanation / Answer

The amount of investment made upto First 5 years = $85000

The Value of Investment after 5 years = 85000 * PVAF ( 10% , 5 ) = 85000*5.6156 = $ 477326.85

Now the amount Invested per year = 85000/2 = 42500$

Now they Want Money at retirement = $3000000

Therefore equation = 477326.85 *FVF(10%,n) + 42500*FVAF(10%,n) = $3000000

Now n can be find out by hit and trial method through calculator

We find n = 13.85 years approx so we take 14 years complete round off.

Answer (a) The Retirement age = 21 + 5 + 14 = 40 Years

Answer (b) IF they Raise 5000 Per year then the additional money they have at the age of retirement is

= 85000 + 5000 = 90000

= 42500 + 5000 = 47500

Now the amount at the time of retirement is =

at the age of 26 amount is = 90000*PVAF(10%,5) = 90000*5.615 = 505405$

Now at the age of 40 amount is = 505405*PVF(10%,14) + 47500*PVAF(10%,14)

= 505405*3.797 + 47500*29.67

= 1919023.924+ 1409442.88 = 3328466.80$

The additional Amount they have at the time of retirement is 328466.80$

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