Answer :
Here is the solution of the given problem above.
Given that the estimated cost of the Hummer is $28,000, and that she invests $12,000 with a 6% rate compounded semiannually. Semiannually, that would be twice a year, so it is the rate every 6 months. Let's get the 6% of $12,000 and it would be $720. Therefore, she will pay a total of $13,440 in a year. Hope this answer helps.
Given that the estimated cost of the Hummer is $28,000, and that she invests $12,000 with a 6% rate compounded semiannually. Semiannually, that would be twice a year, so it is the rate every 6 months. Let's get the 6% of $12,000 and it would be $720. Therefore, she will pay a total of $13,440 in a year. Hope this answer helps.
Answer:
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