Respuesta :
Answer:
The account balance six months from today is $5,187.5.
Step-by-step explanation:
This is a compound interest problem
The compound interest formula is given by:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.
In this problem, we have that
The total amount formula changes after 6 years, at which point each of the principal(initial money), interest rate, and n changes.
This item asks only the balance six months from today, so we use the information given for the first 6 years.
A is the account balance, the value we hope to find.
The loan is of $5,000. So [tex]P = 5,000[/tex]
The account earns 7.5% per annum compounded half yearly, so [tex]r = 0.075, n = 2[/tex].
We want to find the account balance in 6 months. However, t is measured in years. So [tex]t = \frac{6}{12} = 0.5[/tex]
Solving the equation:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A = 5,000(1 + \frac{0.075}{2})^{1}[/tex]
[tex]A = 5,187.5[/tex]
The account balance six months from today is $5,187.5.
