Question

Dr. J. wants to buy a Dell computer that will cost $3,000 three 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 an 8% annual return. How much should he set aside beginning a year from now?

The last part of the question is tripping me up. Thanks.

Answer 1

We have to find out the amount at the end of each year to accumulate $3000 after 3 years. And the payments will start beginning a year from now. It means that the first payment will be made after the end of one year from now (or first year). For calculating this amount, we will use the following formula of future value of annuity.

Future value of annuity = P * ((1 + r)ⁿ - 1/ r)

where, P = periodic payment, r = rate of interest = 8% and n is the time period = 3 years

Now, putting the values in the above formula, we get,

$3000 = P * ((1+8%)³  - 1 ) / 8%)

$3000 = P * ((1+ 0.08)³  - 1 ) / 0.08)

$3000 = P * ((1.08)³  - 1 ) / 0.08)

$3000 = P * ((1.259712  - 1 ) / 0.08)

$3000 = P * (0.259712 / 0.08)

$3000 = P * 3.2464

P = $3000 / 3.2464

P = $924.100

So we need to set aside the amount of $924.100 at the end of each year for 3 years to accumulate $3000.