Question

Cody invests $1,021 in a retirement account with a fixed annual interest rate of 8% compounded 3 times per year. What will the account balance be after 15 years?

a. $2,674.71
b. $2,924.89
c. $3,276.52
d. $3,488.16

Answer 1

To calculate the account balance after 15 years, use the compound interest formula A = P(1 + r/n)^(nt), where P is the initial investment, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the account balance will be $2,924.89.

Step-by-step explanation:

To calculate the account balance after 15 years with an 8% annual interest rate compounded three times per year, the compound interest formula A = P(1 + r/n)^(nt) is applied. Here, P is the initial investment ($1,021), r is the interest rate (0.08), n is the compounding frequency (3), and t is the time in years (15). Plugging in these values yields A = 1021(1 + 0.08/3)^(3*15) = $2,924.89.

This signifies that the account balance after the specified period will be $2,924.89, showcasing the impact of compounding frequency on the growth of an investment over time. The formula considers the compounding effect, crucial in accurately estimating the final balance for compound interest scenarios.