The solution to this problem requires time value of money calculations.Reference to Tables 9-1 through 9-4 in the text is necessary to complete the calculations.
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Denise wants to help pay for her niece's college tuition.Her niece will begin college in one year.How much would Denise need to put into a savings account today at 6% so that her niece can withdraw $10,000 per year for four years and reduce the account balance to zero at the end of the four years?
A)$31,680
B)$34,650
C)$37,600
D)$37,720

Question

The solution to this problem requires time value of money calculations.Reference to Tables 9-1 through 9-4 in the text is necessary to complete the calculations. 
-
Denise wants to help pay for her niece's college tuition.Her niece will begin college in one year.How much would Denise need to put into a savings account today at 6% so that her niece can withdraw $10,000 per year for four years and reduce the account balance to zero at the end of the four years?
A)$31,680
B)$34,650
C)$37,600
D)$37,720

Quizplus · Accepted Answer

Using Table 9-2 (Future Value of an Annuity of $1), we can find that at 6% for four years, the future value of an annuity of $1 is 4.374. 
Using Table 9-1 (Present Value Interest Factor of $1), we can find that at 6% for one year, the present value of $1 is 0.9434.

We can calculate the present value of the annuity using the formula:

Present value = Annual withdrawal amount x (1 - 1 / (1 + interest rate)n / interest rate)

where n is the number of years of the annuity.

Plugging in the values, we get:

Present value = $10,000 x (1 - 1 / (1 + 0.06)4 / 0.06)
Present value = $34,650

Therefore, Denise would need to put $34,650 into a savings account today at 6% to allow her niece to withdraw $10,000 per year for four years and reduce the account balance to zero at the end of the four years.

The Solution to This Problem Requires Time Value of Money