Gracie shay wants to buy a new hummer in five years. gracie estimates the cost of the hummer will be $28,000. if she invests $12,000 now at a rate of 6% compounded semiannually, she:

Option 4 is correct

Step-by-step explanation:

The complete question is as follows:

Gracie Shay wants to buy a new Hummer in 5 years. Gracie estimates the cost of the Hummer will be $28,000. If she invests $12,000 now, at a rate of 6 percent compounded semiannually, she:

1.Will have enough money

2.Will have exactly $16,000

3.Will have $18,000

4.Will have $16,126.80

5.None of these

Solution:-

- The plan is to buy a new Hummer that costs C = $28,000 in t = 5 years.

- She invests P = $12,000 now at an interest rate i = 6% compounded semi-annually.

- We will calculate the amount of money, (compound interest formula), that Gracie has at the end of 5 years:

                    A = P*( 1 + i )^n

- Where, A : Amount after n periods.

               n : Compounding period in years.

- The compounding period (n) is denoted as the number of time the interest in compounded over the time period t. Since the interest is compounded semi-annually then the compounding period would be:

               n = t* ( 2 periods / year )

               n = 5*2 = 10 periods.

- Now use the above "compounded interest" formula for i to be distributed for the whole year i.e half of 6%:

               A = (12,000)*( 1 + 6/200)^10

               A = 12,000*(1.03)^10

               A = $16126.99

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step-by-step explanation: