dr. j wants to buy a dell computer which will cost 2788 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
Please check the cost of the computer.
Do you mean $2,788.00?
yes $2,788.00 :-)
To determine how much Dr. J should set aside at the end of each year, we can use the formula for the future value of an ordinary annuity:
Future Value = Payment × ((1 + Interest Rate) ^ Number of Periods - 1) / Interest Rate
In this case, the future value is $2,788, the interest rate is 7%, and the number of periods is 4 years. We need to solve for the payment.
Rearranging the formula to solve for the payment:
Payment = Future Value × Interest Rate / ((1 + Interest Rate) ^ Number of Periods - 1)
Substituting the given values into the formula:
Payment = $2,788 × 0.07 / ((1 + 0.07) ^ 4 - 1)
Calculating the value:
Payment = $2,788 × 0.07 / (1.07^4 - 1)
Now, let's evaluate the equation step by step:
1. Calculate the value inside the parentheses:
1.07^4 = 1.3108 (rounded)
2. Subtract 1 from the result:
1.3108 - 1 = 0.3108
3. Divide the initial amount by the result obtained in step 2:
$2,788 × 0.07 / 0.3108 ≈ $624.50
Therefore, Dr. J should set aside approximately $624.50 at the end of each year in order to accumulate $2,788 in 4 years, assuming a 7% annual return.