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IgorLugansk [536]
3 years ago
13

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?
Business
1 answer:
andre [41]3 years ago
4 0
<span>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

</span>
<span><span>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


 
</span> How much will Melanie's investment be worth in 8 years?</span>


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