in order to start a small business, a student takes out a simple interest loan for $6000.00 for 6 months at…

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 11.25%. a. how much interest must the student pay? b. find the future value of the loan. a. the amount of interest is $ (round to the nearest cent as needed.)

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 11.25%. a. how much interest must the student pay? b. find the future value of the loan. a. the amount of interest is $ (round to the nearest cent as needed.)

Answer

Explanation:

Step1: Identify the formula for simple - interest

The formula for simple interest is $I = Prt$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years.

Step2: Convert the given values to the correct form

The principal amount $P=$6000$, the annual interest rate $r = 11.25%=0.1125$, and the time $t=\frac{6}{12}=0.5$ years.

Step3: Calculate the simple interest

Substitute the values into the formula: $I = 6000\times0.1125\times0.5$. $I=6000\times0.1125\times0.5 = 337.5$

Step4: Calculate the future value of the loan

The formula for the future value $A$ of a simple - interest loan is $A=P + I$. Since $P = 6000$ and $I = 337.5$, then $A=6000 + 337.5=6337.5$

Answer:

a. The amount of interest is $$337.50$ b. The future value of the loan is $$6337.50$