Question

Assume that your parents wanted to have $70,000 saved for college by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 9.0% per year on their investments.

a. How much would they have to save each year to reach their​ goal?

b. If they think you will take five years instead of four to graduate and decide to have $110,000 saved just in​ case, how much would they have to save each year to reach their new​ goal?

Answer 1

a. The amount is computed as follows:

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

$ 70,000 = Annual savings x [ [ (1 + 0.09)¹⁸ - 1 ] / 0.09 ]

$ 70,000 = Annual savings x [ [ 4.717120417 - 1 ] / 0.09 ]

$ 70,000 = Annual savings x 41.30133797

Annual savings = $ 70,000 / 41.30133797

Annual savings = $ 1,694.86 Approximately

b. The amount is computed as follows:

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

$ 110,000 = Annual savings x [ [ (1 + 0.09)¹⁸ - 1 ] / 0.09 ]

$ 110,000 = Annual savings x [ [ 4.717120417 - 1 ] / 0.09 ]

$ 110,000 = Annual savings x 41.30133797

Annual savings = $ 110,000 / 41.30133797

Annual savings = $ 2,663.35 Approximately

Please ask in case of any doubts.