a restaurant borrows $15,200 from a local ban...
a restaurant borrows $15,200 from a local bank for 7 months. the local bank charges simple interest at an annual rate of 4.55% for this loan. assume each month is 1/12 of a year. answer each part below. do not round any intermediate computations, and round your final answers to the nearest cent. if necessary, refer to the list of financial formulas. (a) find the interest that will be owed after 7 months. (b) assuming the restaurant doesnt make any payments, find the amount owed after 7 months.
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.
Given $P=\$15200$, $r = 0.0455$ (since $4.55\%=0.0455$), and $t=\frac{7}{12}$ years.
## Step2: Calculate the interest
$I=Prt=15200\times0.0455\times\frac{7}{12}$
$I = 15200\times0.0455\times\frac{7}{12}=\frac{15200\times0.0455\times7}{12}$
$15200\times0.0455 = 691.6$
$691.6\times7 = 4841.2$
$I=\frac{4841.2}{12}\approx403.43$
## Step3: Calculate the amount owed
The amount $A$ owed is the sum of the principal $P$ and the interest $I$. So $A=P + I$.
$A=15200+403.43 = 15603.43$
# Answer:
(a) $\$403.43$
(b) $\$15603.43$