Dr. J. wants to buy a Dell computer which will cost $2,788 four years from today. He would like to set aside an equal amount at the end of each year in order to accumulate the amount needed. He can earn 7% annual return. How much should he set aside?
627.93
To calculate the equal amount that Dr. J. needs to set aside each year, we can use the concept of present value. Present value calculates the current value of a future cash flow by discounting it at a given interest rate. In this case, we want to find the equal annual payment that will accumulate to $2,788 in four years at a 7% annual return.
The formula to calculate the present value of an equal annual payment is:
PV = PMT × [(1 - (1/(1 + r)^n)) / r],
where:
PV = Present Value (the desired future amount, which is $2,788 in this case)
PMT = Equal annual payment
r = Interest rate per period (annual return rate divided by the number of compounding periods per year)
n = Number of periods (in this case, four years)
First, let's convert the annual return rate to a periodic rate by dividing it by the number of compounding periods per year, assuming the compounding is annually.
r = 7% / 1 = 7% = 0.07
Now, we can substitute the values into the formula and solve for PMT:
2,788 = PMT × [(1 - (1/(1 + 0.07)^4)) / 0.07]
To solve this equation, we can follow these steps:
1. Calculate the term inside the brackets first:
(1 - (1/(1 + 0.07)^4)) / 0.07 = 3.3522
2. Divide both sides of the equation by 3.3522:
2,788 / 3.3522 = PMT
After performing the calculation, we find that PMT ≈ $831.72.
Therefore, Dr. J. should set aside approximately $831.72 at the end of each year in order to accumulate enough to buy the Dell computer costing $2,788 in four years with a 7% annual return.