QuestionA print shop borrows \$5100 for 356 days at 6.5% simple interest. Calculate (a) interest owed and (b) total amount owed.

Studdy Solution

STEP 1

Assumptions1. The borrowed amount is $5100. The interest rate is6.5%<br />3. The time for repayment is356 days4. Each day is considered as$ \frac{1}{365}$ of a year5. The interest is calculated as simple interest, not compounding6. The print shop doesn't make any payments during the356 days

STEP 2

First, we need to find the interest amount on the borrowed sum. We can do this by using the formula for simple interest which is $Interest = Principal\, amount \\times Interest\, rate \\times Time$

STEP 3

Now, plug in the given values for the principal amount, interest rate, and time to calculate the interest.
$Interest = \$5100 \\times6.5\% \\times \frac{356}{365}$

STEP 4

Convert the percentage to a decimal value.
$6.\% =0.065$ $Interest = \$5100 \\times0.065 \\times \frac{356}{365}$

STEP 5

Calculate the interest amount.
$Interest = \$5100 \\times0.065 \\times \frac{356}{365} = \$612.60$ This is the answer to part (a). The print shop will owe $612.60 in interest after356 days.

STEP 6

Now that we have the interest amount, we can find the total amount the print shop has to pay back. This includes both the borrowed amount and the interest.
$Total\, amount = Principal\, amount + Interest$

STEP 7

Plug in the values for the principal amount and the interest to calculate the total amount.
$Total\, amount = \$5100 + \$612.60$

STEP 8

Calculate the total amount the print shop has to pay back.
$Total\, amount = \$5100 + \$612.60 = \$5712.60$ This is the answer to part (b). The print shop will owe $5712.60 after356 days if no payments are made.

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