Sanka Blunck wants to receive $8,000 each year for 20 years. How much must Sanka invest today at 4% interest compounded annually? (p. 324)
To find out how much Sanka must invest today, we can use the formula for the present value of an annuity. The formula is:
PV = PMT * ((1 - (1 + r)^(-n)) / r)
where:
PV = Present value (the amount Sanka must invest today)
PMT = Payment amount Sanka wants to receive each year ($8,000)
r = Interest rate per compounding period (4% per year)
n = Number of compounding periods (20 years)
Using this formula, we can substitute the given values:
PV = $8,000 * ((1 - (1 + 0.04)^(-20)) / 0.04)
Now, let's calculate the value:
PV = $8,000 * ((1 - (1.04)^(-20)) / 0.04)
= $8,000 * ((1 - 0.4564) / 0.04)
= $8,000 * (0.5436 / 0.04)
= $8,000 * 13.59
= $108,720
Therefore, Sanka must invest $108,720 today at a 4% interest rate compounded annually in order to receive $8,000 each year for 20 years.