Art Newner wants to know how much he will have to invest today in order to receive an annuity of $8,000 for three years if interest is earned at 10 percent annually. He will make all his withdrawals at end of each year. How much should Art invest? (Using the Calculator)
To calculate how much Art should invest today in order to receive an annuity of $8,000 for three years with an annual interest rate of 10 percent, we can use the formula for the present value of an ordinary annuity. The formula is:
PV = PMT * [(1 - (1 + r)^(-n)) / r]
Where PV is the present value, PMT is the annuity payment, r is the interest rate per period, and n is the number of periods.
In this case, the annuity payment (PMT) is $8,000, the interest rate (r) is 10 percent (or 0.10 as a decimal), and the number of periods (n) is 3 years.
Using a financial calculator or spreadsheet program, we can plug in these values and calculate the present value:
PV = $8,000 * [(1 - (1 + 0.10)^(-3)) / 0.10]
PV = $8,000 * [(1 - (1.10)^(-3)) / 0.10]
PV = $8,000 * [(1 - 0.7513) / 0.10]
PV = $8,000 * [0.2487 / 0.10]
PV = $8,000 * 2.487
PV = $19,896
Therefore, Art should invest approximately $19,896 today in order to receive an annuity of $8,000 for three years with an annual interest rate of 10 percent.