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Jim Moore opens a new savings account. He deposits $12,000 at 12% compounded semiannually. At the start of the fourth year, Jim deposits an additional $50,000 that is also compounded semiannually at 12%. At the end of six years, the balance in Jim Moore's account is

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Verified Answer :

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:

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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:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(A_1(6) = 12000\left(1 + \frac{0.12}{6}\right)^{2 \times 6}\)

\(A_1(6) = 15219\)

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:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(A_2(2) = 50000\left(1 + \frac{0.12}{6}\right)^{2 \times 2}\)

\(A_2(2) = 54122\)

Hence, the balance in dollars will be given by:

\(A(6) = A_1(6) + A_2(2) = 15219 + 54122 = 69341\)

More can be learned about compound interest at https://brainly.com/question/25781328

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