in order to start a small business, a student takes out a simple - interest loan for $9000 for 3 months at a…
in order to start a small business, a student takes out a simple - interest loan for $9000 for 3 months at a rate of 7.75%. a. how much interest must the student pay? b. find the future value of the loan.
Answer
Explanation:
Step1: Recall simple - interest formula
The simple - interest formula 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. $P=$9000$, $r = 7.75%=0.0775$, and $t=\frac{3}{12}=0.25$ years. $I = Prt=9000\times0.0775\times0.25$
Step2: Calculate the interest
$I = 9000\times0.0775\times0.25=$174.375$
Step3: Recall future - value formula
The future - value formula for simple interest is $A=P + I$, where $A$ is the future value, $P$ is the principal, and $I$ is the interest. $A=9000 + 174.375=$9174.375$
Answer:
a. The student must pay $$174.38$ in interest. b. The future value of the loan is $$9174.38$