Questions: The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Answer parts (a) and (b). Principal Rate Compounded Time 6000 0.5 % quarterly 5 year a. Find how much money there will be in the account after the given number of years. The amount of money in the account after 5 years is (Round to the nearest cent as needed.) b. Find the interest earned. The amount of interest earned is (Round to the nearest cent as needed.)

The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Answer parts (a) and (b). Principal Rate Compounded Time 6000 0.5 % quarterly 5 year a. Find how much money there will be in the account after the given number of years. The amount of money in the account after 5 years is (Round to the nearest cent as needed.) b. Find the interest earned. The amount of interest earned is (Round to the nearest cent as needed.)
Transcript text: The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Answer parts (a) and (b). Principal & Rate & Compounded & Time $6000$ & $0.5 \%$ & quarterly & 5 year a. Find how much money there will be in the account after the given number of years. The amount of money in the account after 5 years is $\$$ $\square$ (Round to the nearest cent as needed.) b. Find the interest earned. The amount of interest earned is $\$$ $\square$ (Round to the nearest cent as needed.)
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Solution

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Solution Steps

Step 1: Convert the annual interest rate from a percentage to a decimal

To convert the annual interest rate to a decimal, we divide the rate by 100. Thus, \(r = 0.5 / 100 = 0.0.5\).

Step 2: Use the compound interest formula to calculate the future value \(A\)

The formula to calculate the future value \(A\) is given by \(A = P(1 + \frac{r}{n})^{nt}\), where \(P = 6000\), \(r = 0.0.5\), \(n = 4\), and \(t = 5\). Substituting the values, we get \(A = 6000 \times (1 + \frac{0.0.5}{4})^{4 \times 5} = 6151.79\).

Step 3: Calculate the interest earned

The interest earned over the period is the future value minus the principal, which is \(A - P = 6151.79 - 6000 = 151.79\).

Final Answer:

The future value of the investment after 5 years is $6151.79, and the interest earned over this period is $151.79.

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