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?

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