Solve using Engineering Economics way: 6) (40 points) An OSU alumna wants to est

Question

Solve using Engineering Economics way:

6) (40 points) An OSU alumna wants to establish a scholarship fund and is planning to make the following cash contributions- an initial contribution now followed by 5 annual contributions. She just contributed $100,000. One year from now she plans to contribute S20,000 and then continue to contribute an amount $10,000 greater than the previous contribution annually until a total of 5 annual contributions are made. Determine the annual scholarship amount this fund can support over a 20-year period, if the first withdrawal is made exactly 6 years from now. The fund is expected to earn 10% per year compounded annually.

Explanation / Answer

Contributions made each year will be $100000,$20000,$30000,$40000 and $50000

Then future worth of this payment will be

100000(1.1)^5+20000(1.1)^4+30000(1.1)^3+40000(1.1)^2+50000(1.1)=$333,663

Now assume the amount A to be withdeawn each year for 20 eyars

A+A/(1.1)+A/(1.1)^2+...A/(1.1)^20=333,663 because present worth of future payment will be equal to intial amount as it will be 0 in account after 20 years

A[1+{1/1.1}+1/{1.1)^2+...+1/(1.1)^20]=333663

A=$35410.72

Hence the amount withdrawn each year is $35410.72

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