Respuesta :
Using compound interest, it is found that the the end of six years, the balance in Jim Moore's account is $69,341.
What is compound interest?
The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
- A(t) is the amount of money after t years.
- 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 year.
In this problem, the account is divided into two separate investments. The first one is of $12,000 at 12% compounded semiannually, for 6 years. Hence the parameters are:
P = 12000, r = 0.12, n = 2, t = 6.
Hence the amount in 6 years is of:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A_1(6) = 12000\left(1 + \frac{0.12}{6}\right)^{2 \times 6}[/tex]
[tex]A_1(6) = 15219[/tex]
The second investment is of $50,000 that is also compounded semiannually at 12%, at the end of the fourth year, which will be compounded for 6 - 4 = 2 years, hence the amount will be of:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A_2(2) = 50000\left(1 + \frac{0.12}{6}\right)^{2 \times 2}[/tex]
[tex]A_2(2) = 54122[/tex]
Hence, the balance in dollars will be given by:
[tex]A(6) = A_1(6) + A_2(2) = 15219 + 54122 = 69341[/tex]
More can be learned about compound interest at https://brainly.com/question/25781328
