Question

julie borrowed $6,650 for 8 months from a bank. the bank discounted the loan at 5.5%.
a. how much interest did julie pay the bank for the use of its money?
b. how much did she receive from the bank?
c. what was the actual rate of interest she paid?
a. the interest is $\square$.
(round to the nearest cent as needed.)

Explanation:

Step1: Calculate discount interest

Use simple discount formula: $I = P \times r \times t$
$P = 6650$, $r = 0.055$, $t = \frac{8}{12}$
$I = 6650 \times 0.055 \times \frac{8}{12}$

Step2: Compute proceeds (amount received)

Proceeds = Principal - Interest
$A = 6650 - I$

Step3: Find actual interest rate

Use $r_{actual} = \frac{I}{A \times t}$
$r_{actual} = \frac{I}{A \times \frac{8}{12}}$

Answer:

a. The interest is $\$243.83$.
b. She received $\$6406.17$ from the bank.
c. The actual rate of interest is approximately 5.70%.