a print shop borrows $4200 from a credit union for 178 days. the credit union charges simple interest at an…

a print shop borrows $4200 from a credit union for 178 days. the credit union charges simple interest at an annual rate of 6.5% for this loan. assume each day is $\frac{1}{365}$ 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 178 days. (b) assuming the print shop doesnt make any payments, find the amount owed after 178 days.

a print shop borrows $4200 from a credit union for 178 days. the credit union charges simple interest at an annual rate of 6.5% for this loan. assume each day is $\frac{1}{365}$ 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 178 days. (b) assuming the print shop doesnt make any payments, find the amount owed after 178 days.

Answer

Explanation:

Step1: Identify the 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.

Step2: Convert the annual interest rate to decimal form

Given $r = 6.5%=0.065$.

Step3: Calculate the time in years

Given the time is 178 days and each day is $\frac{1}{365}$ of a year, so $t=\frac{178}{365}$.

Step4: Calculate the interest

$P = 4200$, $r = 0.065$, $t=\frac{178}{365}$, then $I=Prt=4200\times0.065\times\frac{178}{365}$ $I = 4200\times0.065\times\frac{178}{365}=\frac{4200\times0.065\times178}{365}=\frac{4200\times11.57}{365}=\frac{48594}{365}\approx133.134247$ Rounding to the nearest cent, $I\approx$133.13$.

Step5: Calculate the amount owed

The amount owed $A$ is the sum of the principal $P$ and the interest $I$. So $A=P + I$. Since $P = 4200$ and $I\approx133.13$, then $A=4200 + 133.13=$4333.13$.

Answer:

(a) $$133.13$ (b) $$4333.13$