Question

a man borrowed $3400 from a bank for 9 months. a friend was cosigner of the mans personal note. the bank collected $8\frac{1}{2}%$ simple interest on the date of maturity.
a) how much did the man pay for the use of the money?
b) determine the amount he repaid to the bank on the due date of the note.

a) the man paid $\square$ for the use of the money.

Explanation:

Step1: Convert rate and time

First, convert the mixed number interest rate to a decimal: $8\frac{1}{2}\% = 0.085$. Convert time to years: $9$ months $=\frac{9}{12}=0.75$ years.

Step2: Calculate simple interest

Use the simple interest formula $I = P \times r \times t$, where $P=\$3400$, $r=0.085$, $t=0.75$.
$I = 3400 \times 0.085 \times 0.75$
$I = 3400 \times 0.06375$
$I = 216.75$

Step3: Calculate total repayment

Add principal and interest: $A = P + I$
$A = 3400 + 216.75 = 3616.75$

Answer:

a) $\$216.75$
b) $\$3616.75$