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?
A. $823.15
B. $531.81
C. $627.93
D. $697.00
A. $823.15
To determine how much Dr. J should set aside each year, we need to calculate the annual amount that, when compounded at a 7% annual return, will accumulate to $2,788 over a period of four years.
This can be done using the future value of an ordinary annuity formula:
Future Value = Annual Contribution * [(1 + Interest Rate)^Number of Years - 1] / Interest Rate
In this case,
Future Value = $2,788
Interest Rate = 7% or 0.07 (expressed as a decimal)
Number of Years = 4
Let's calculate the amount Dr. J should set aside using each of the given options:
Option A: $823.15
Future Value = $823.15 * [(1 + 0.07)^4 - 1] / 0.07 ≈ $823.15 * [1.310796 - 1] / 0.07 ≈ $823.15 * 0.310796 / 0.07 ≈ $823.15 * 4.439942857 ≈ $3,471.71
Option B: $531.81
Future Value = $531.81 * [(1 + 0.07)^4 - 1] / 0.07 ≈ $531.81 * [1.310796 - 1] / 0.07 ≈ $531.81 * 0.310796 / 0.07 ≈ $531.81 * 4.439942857 ≈ $2,364.43
Option C: $627.93
Future Value = $627.93 * [(1 + 0.07)^4 - 1] / 0.07 ≈ $627.93 * [1.310796 - 1] / 0.07 ≈ $627.93 * 0.310796 / 0.07 ≈ $627.93 * 4.439942857 ≈ $2,789.98
Option D: $697.00
Future Value = $697.00 * [(1 + 0.07)^4 - 1] / 0.07 ≈ $697.00 * [1.310796 - 1] / 0.07 ≈ $697.00 * 0.310796 / 0.07 ≈ $697.00 * 4.439942857 ≈ $3,094.28
Based on the calculations, the amount Dr. J should set aside each year to accumulate $2,788 in four years with a 7% annual return is approximately $627.93. Therefore, the correct answer is C. $627.93.