You will receive $225 a month for the next eight years from an insurance settlement. The interest rate is 7% compounded monthly for the first three years and 9% compounded semi-annually (quarterly) for the final five years. What is this settlement worth to you today?

$16,014.64

Explanation:

first we have to determine the present value of the last five years:

effective interest for last 5 years = (1 + 9%/4)⁴ - 1 = 1.093 - 1 = 9.31%

9.31% / 12 = 0.7757%

present value = $225 x 47.82377 (PV annuity factor, 0.7757%, 60 periods) = $10,760.35

now, present value = $10,760.35 / (1 + effective interest)³

effective interest first 3 years = (1 + 7%/12)¹² - 1 = 1.0723 - 1 = 7.23%

present value = $10,760.35 / (1 + 7.23%)³ = $8,727.25

now we need to determine the present value of the first 3 years:

present value = $225 x 32.38838 (PV annuity factor, 2.25%, 36 periods) = $7,287.39

total value of the annuity = $16,014.64

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