A man wants to help provide a college education for his young daughter. He can afford to invest $1500/yr for the next 5 years, beginning on the girl 's 5th birthday. He wishes to give his daughter $10,000 on her 18th, 19th , 20th, and 21 st birthdays, for a total of $40,000. Assuming 6% interest, what uniform annual investment will he have to make on the girl's 9th through 17th birthdays?

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jepessoa jepessoa · Answer 1 · 2021-06-02T03:15:24+02:00

Answer:

$1,919.69

Explanation:

when the daughter is 9 years old, total savings = $1,500 x 5.6371 (FVIFA, 6%, 5 periods) = $8,455.65

first 5 payments:

birthdays = 5, 6, 7, 8, 9

the present value of the $40,000 that he needs for her daughter's college = $10,000 x 3.4651 (PVIFA, 6%, 4 periods) = $34,651

the FV until the 17th birthday = $8,455.65 x 1.06⁸ = $15,650.82

he needs to save = $34,651 - $15,650.82 = $19,000.18

value of annual deposits = $19,000.18 / 9.8975 (FVIFA, 6%, 8 peridos) = $1,919.69