Final answer:
To find the account balance after 13 years with monthly compounded interest, one uses the compound interest formula A = P(1 + r/n)^(nt), substituting the given values for P ($5,000), r (6% or 0.06), n (12), and t (13). The computed balance reflects the impact of compound interest over the period.
Step-by-step explanation:
To compute the balance in an account after a certain period of time with compound interest, we can use the compound interest formula, which is A = P(1 + \frac{r}{n})^{nt}. Here, A is the amount of money accumulated after n years, including interest. P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
In this case, the principal amount P is $5,000, the annual interest rate r is 6% or 0.06, the number of times interest is compounded per year n is 12 (since it is monthly compounding), and the time t is 13 years.
Step-by-Step Calculation:
- Convert the annual interest rate from a percentage to a decimal: r = 6% = 0.06.
- Determine the number of times interest is compounded per year: n = 12.
- Substitute these values into the compound interest formula: A = $5,000 \times (1 + \frac{0.06}{12})^{12 \times 13}.
- Calculate the parentheses and exponent: A = $5,000 \times (1 + 0.005)^{156}.
- A = $5,000 \times (1.005)^{156}
- Compute the final balance using a calculator.
After calculating, we can find the balance in the account after 13 years.