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James and his wife would like to retire in 23 years. Upon retirement they want to...

James and his wife would like to retire in 23 years. Upon retirement they want to spend the first 10 years traveling around the world. To travel in the style they are accustomed they will require $65,000 in each of the 10 years. Their first payment of $65,000 will be 23 years from today and there will be 10 total yearly payments of $65,000. After the years of traveling they then want to live in a small retirement village in Charleston. For living expenses they would like to receive yearly income of $50,000 per year in each of the next 25 years after they finish traveling (a total of 25 yearly $50,000 payments with their first payment beginning the year after their quit traveling).
In order to save up for these expenses, assume that James and his wife plan to deposit the same amount of money for the next 15 years (with the first deposit being one year from today) in an account paying 9% interest compounded annually (they don’t want to be burdened with saving money the last few years before they retire). Calculate the amount of their annual deposits so that when they receive their last $50,000 payment there will be a zero balance in the account.

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Expert Solution

Solution.>

The correct answer is $10,995.54

I have solved this question in Excel. The formula used are written along with the values. If you still have any doubt, kindly ask in the comment section.

Firstly we have to find the amount they must have after 32 years from now so that it could give 25 annual payments of $50,000. Hence we calculate the PV at 32 years from now. Then we find the Present value at 15 years from now using the answer.

Secondly we have to find the amount they must have after 23 years from now so that it could give 10 annual payments of $65,000. Hence we calculate the PV at 23 years from now. Then we find the Present value at 15 years from now using the answer.

Then we add both the answers to get the total PV at 15 years from now.

This PV calculated above will now become the Future Value in calculating the annual payments for the next 15 years from now.

The formula used in excel is = PMT(Rate,NPER,PV,-FV)

It has been shown in the excel below.

Note: Give it a thumbs up if it helps! Thanks in advance!

jeff jeffy answered 1 year ago
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