19. Beth saves $2,500 a year from age 25 until age 34 (inclusive) and invests the money in an account earning 5% annually. Beth stops investing at age 34, but does not withdraw the accumulation until age 65. In contrast, Bill saves $2,500 a year from age 35 until age 65 inclusively and invests in a similar account to Beth, earning 5% annually. Bill will have accumulated significantly more than Beth at age 65. True False

True

Explanation:

future value of an annuity = payment x {[(1 + r)ⁿ - 1] / r}

future value with compound interest = present value x (1 + r)ⁿ

by age 65 Beth will have:

FV at 34 = $2,500 x {[(1 + 5%)¹⁰ - 1] / 5%} = $2,500 x 12.5779 = $31,445

FV at 65 = $31,445 x (1 + 5%)³¹ = $142,699

by age 65 Bill will have:

FV at 65 = $2,500 x {[(1 + 5%)³⁰ - 1] / 5%} = $2,500 x 66.4388 = $166,097

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