Question

Cynthia invested $12,000 in a savings account. if the interest rate is 6% per year, how much will be in the account in 10 years for quarterly compounding? Round your answer to the nearest cent. Do NOT round until you calculate the final answer

Answer 1

To calculate compound interest, we use the formula A = P(1 + r/n)^(nt). In this case, Cynthia invested $12,000 with an interest rate of 6% annually and quarterly compounding. After calculating the expression inside the parentheses and raising it to the power of 40, we find that the amount in the account after 10 years will be $20,323.48.

Step-by-step explanation:

To calculate compound interest, we can use the formula:

A = P(1 + r/n)^(nt)

Where:

• A is the future value of the investment
• P is the principal amount (initial investment)
• r is the annual interest rate (in decimal form)
• n is the number of times interest is compounded per year
• t is the number of years

In this case, Cynthia invested $12,000 with an interest rate of 6% annually and quarterly compounding. So we have:

A = 12000(1 + 0.06/4)^(4*10)

Calculating the expression inside the parentheses first:

A = 12000(1 + 0.015)^(40)

Next, raise the expression to the power of 40:

A = 12000(1.015)^(40)

Finally, multiply the result by the initial investment:

A = 12000 * 1.6936232878

Rounding to the nearest cent, the final answer is $20,323.48.