Question

In each of the following compound interest equations with t representing the account term, determine the number of times the account is compounded per year and the interest rate percent.

2254 = 2000(1.002)¹²ᵗ

Answer 1

In the compound interest equation provided, the account is compounded monthly (12 times per year), and the interest rate percent is 0.2% per month, which equates to 2.4% annually.

Step-by-step explanation:

To find the number of times the account is compounded per year and the interest rate percent in the compound interest equation 2254 = 2000(1.002)^12t, we need to understand the general formula for compound interest, which is of the form A = P(1+r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (in decimal form).
• n is the number of times the interest is compounded per year.
• t is the time the money is invested for, in years.

Comparing the given equation to the general formula, we have an annual interest rate (r) of 0.002 (or 0.2%) and n, the number of times the interest is compounded per year, is 12. Hence, the account is compounded monthly, and the interest rate is 0.2% per month or 2.4% per annum.