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10 May, 18:21

Melanie invested $12,200 at 4.8% interest compounded semiannually and she wants to know how much her investment will be worth in 8 years.

What is the periodic interest rate of Melanie's investment?

How many compounding periods does Melanie's investment offer in a year? How about in 8 year?

What expression can Melanie write to figure out how much her investment will be worth in 8 years?

How much will Melanie's investment be worth in 8 years?

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  1. 10 May, 20:32
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    What is the periodic interest rate of Melanie's investment?

    How many compounding periods does Melanie's investment offer in a year? How about in 8 year?

    Semiannually means that it is twice in a year, then:

    - the number of compounding periods in a year is 2.

    - the number of compounding periods in 8 years is 2 * 8 = 16

    What expression can Melanie write to figure out how much her investment will be worth in 8 years?

    Use the formula : F = P * (1 + r/n) ^ (n*t)

    P is the initial investment = $12,000

    n = the number of periods per year, which is 2

    r is the yearly rate = 4.8% = 0.048

    t is the number of years, which is 8.

    Then, the equation is F = $12,000 * (1 + 0.048/2) ^ (8*2) =

    = $12,000 (1 + 0.024) ^ 16 = $12,000 (1,024) ^16

    How much will Melanie's investment be worth in 8 years?

    Just use the calculator: 12,000 (1,024) ^16 = $17,538
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