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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

...?

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The answer is no. 4 "Will have $16,126.80". Below is the solution:

12000 ( 1 + 6/200)^10 = 16,126.80 $ 

Answer:

Option 4 - She will have $16,126.80

Step-by-step explanation:

Given : 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.

To find : Which option she will have ?

Solution :

Using compound interest formula,

\(A=P(1+r)^t\)

Where, A is the amount  

P is the principle P=12,000    

Compounded semiannually,

r is the rate 6%=0.06

\(r=\frac{0.06}{2}=0.03\)

t is the time 5 years

\(t=5\times 2=10\)

Substitute the value,

\(A=P(1+r)^t\)

\(A=(12000)(1+0.03)^{10}\)

\(A=12000\times (1.03)^{10}\)

\(A=12000\times 1.3439\)

\(A=16126.99\)

The amount she will have $16126.99.

Therefore, Option 4 is correct.

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