Suppose, starting at his 25th birthday, Michael deposits $5000 at the beginning
ID: 3544172 • Letter: S
Question
Suppose, starting at his 25th birthday, Michael deposits $5000 at the beginning of every year into a retirement annuity that pays 9% interest per year, compounded annually. He wants to retire when his annuity first reaches or exceeds $1 million. Besides, for a better money management, Michael's annual deposits grow by 6% each year. So the first year he puts in $5000, the second year $5300, the third year $5618, etc.
In how many years will he be able to retire with this plan? Write a Matlab m-file using an While loop. (if necessary, you can use an IF statement) Print the codes and results
Explanation / Answer
line MATLAB Code
1 Balance = 5000; %initialize Balance
2 year = 0; %initialize year counter
3 while Balance < 1000000
4 Balance = (1.09)*Balance + 5000;
5 year = year + 1; %update year counter
6 end
7 year, Balance %This will display the year and the
8 corresponding balance that first broke $1 million.
When this code is entered, the following output results: year = 34.00, Balance = 1078553.77
Thus, Michael will be able to retire at age 59, with a nest egg of $1,078,553.77.
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