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 ??????

Question

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 ??????

gw2011 · Answer

The answer is (4): $16,126.80.  Here is how you get the answer:

A=P(1+i)^n

A=The amount
P=Principal
i=interest rate
n=Number of periods the interest applies

i=0.06/2=0.03  because the interest is compounded semiannually
n=10 because the interest is 3% per period and there are 2 periods per year for 5 years

A=(12,000)(1.03)^10
A=(12,000)(1.3439)
A=$16,126.80

anonymous · Answer

thank you so much

anonymous · Answer

There is a slight difference in doing it differently. the answer for this is 16126.99655. Here is the reason
Calculate the effective annual rate
(1+0.06/2)^2 -1=0.0609 
Now uses the Future value formula
12000(1+0.0609)^5=16126.99655