In order to start a small business, a student takes out a simple interest loan for $\$ 6000.00$ for 6 months at a rate of $11.00 \%$.
a. How much interest must the student pay?
b. Find the future value of the loan.
a. The amount of interest is $\$ \square$.
(Round to the nearest cent as needed.)
b. The future value is $\$$
(Round to the nearest cent as needed.)
Answer
Final Answer: a. The amount of interest is \(\boxed{330.00}\). b. The future value is \(\boxed{6330.00}\).
Step 1 ：Given that the principal amount (P) is $6000, the rate of interest (R) is 11% or 0.11 in decimal form, and the time (T) is 6 months or 0.5 years.
Step 2 ：We can calculate the interest (I) using the formula for simple interest: I = PRT. Substituting the given values, we get I = 6000 * 0.11 * 0.5 = $330.00.
Step 3 ：The future value (FV) of the loan is the sum of the initial loan and the interest. So, FV = P + I = 6000 + 330 = $6330.00.
Step 4 ：Final Answer: a. The amount of interest is \(\boxed{330.00}\). b. The future value is \(\boxed{6330.00}\).
