Question

Ashley is planning to attend college when she graduates from high school 7 years from now. She anticipates that she will need $10,000 at the beginning of each of the four college years to pay for tuition and fees, and have some spending money. Ashley has made an arrangement with her father to do the household chores if her dad deposits $3,500 at the end of each year for the next 7 years in a bank account paying 8 percent interest. Will there be enough money in the account for Ashley to pay for her college expenses? Assume the rate of interest stays at 8 percent during the college years.

Select one:

a. $5,207

b. $4,846

c. $1,524

d. $4,541

Answer 1

The present value of $ 10,000 is computed as shown below:

Present value = Annual payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

= $ 10,000 x [ (1 - 1 / (1 + 0.08)⁴ ) / 0.08 ]

= $ 10,000 x 3.31212684

= $ 33,121.2684

Since the payments are at the beginning of the period, hence we need to multiply the above figure by (1 + 0.08) as shown below:

= $ 33,121.2684 x 1.08

= $ 35,770.96987

The future value of $ 3,500 is computed as shown below:

Future value = Annual payment x [ [ (1 + r)ⁿ – 1 ] / r ]

= $ 3,500 x [ [ (1 + 0.08)⁷ - 1 ] / 0.08 ]

= $ 3,500 x 8.92280336

= $ 31,229.81176

So, the difference in amount is computed as follows:

= $ 35,770.96987 - $ 31,229.81176

= $ 4,541 Approximately

So, the correct answer is option d.

Feel free to ask in case of any query relating to this question