Question

I’m going to put $100,000 into an investment at the beginning of year 1. At the end of year 2, I am going to add $55,000 more to the investment. In year 4, I will start to remove $20,000 per year (on the first day of the year). If the interest rate on the investment is 8.2%/year compounded annually, how long (to the nearest year) before the balance in the investment drops to zero? Work this problem on a spreadsheet using simple and compound interest formulas only.

Answer 1

Answer:

  19 years

Step-by-step explanation:

The attached spreadsheet shows the balance will be zero at the beginning of year 19, when the last $10,423.27 is withdrawn from the account.

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One could argue that the "nearest year" is year 18, when the balance after the withdrawal is less than $10,000.

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In the attached spreadsheet, the ending balance is 1.082 times the beginning balance (after deposits and withdrawals), which is the ending balance of the year before (after deposits).

In year 1 the beginning balance has 100,000 added. In year 2, the ending balance has 55,000 added. In year 4 and every year after, the beginning balance as 20,000 subtracted.