Question

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?

Answer 1

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

Answer 2

Answer: 2.4% to the first question

(since Edufirst answered the other questions correctly, I am only answering the first question "What is the periodic interest rate of Melanie's investment?")

Explanation: The periodic interest rate is the interest rate per period. It can be found by dividing the annual interest rate by the number of periods per year. Since there are two periods and 4.8% is the semiannual compound interest, you divide 4.8% by two. So 4.8% ÷ 2 = 2.4%.