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Solved on Dec 06, 2023

Calculate the total payment to pay off a $500 promissory note with 10% interest and 180-day term. Round to the nearest cent.
$[500×(1+0.10×180365)] \$[500 \times (1 + 0.10 \times \frac{180}{365})]

STEP 1

Assumptions
1. The principal amount of the promissory note is $500.00.
2. The annual interest rate is 10%.
3. The term of the promissory note is 180 days.
4. The interest is calculated using ordinary interest (simple interest), not compounded.
5. The total payment required will include both the principal and the interest.

STEP 2

First, we need to calculate the interest using the formula for simple interest:
Interest=Principal×Rate×TimeInterest = Principal \times Rate \times Time

STEP 3

The interest rate needs to be converted from a percentage to a decimal for calculation purposes:
10%=10100=0.1010\% = \frac{10}{100} = 0.10

STEP 4

The time needs to be expressed in years because the interest rate is an annual rate. Since there are 360 days in a year for ordinary interest calculation, we convert 180 days to a fraction of a year:
Time=Number of days360=180360=0.5 yearsTime = \frac{Number\, of\, days}{360} = \frac{180}{360} = 0.5\, years

STEP 5

Now we can calculate the interest using the principal amount, the decimal interest rate, and the time in years:
Interest=$500.00×0.10×0.5Interest = \$500.00 \times 0.10 \times 0.5

STEP 6

Perform the multiplication to find the interest:
Interest=$500.00×0.10×0.5=$25.00Interest = \$500.00 \times 0.10 \times 0.5 = \$25.00

STEP 7

The total payment required to pay off the promissory note is the sum of the principal amount and the interest:
Total payment=Principal+InterestTotal\, payment = Principal + Interest

STEP 8

Plug in the values for the principal and the interest to calculate the total payment:
Total payment=$500.00+$25.00Total\, payment = \$500.00 + \$25.00

STEP 9

Calculate the total payment:
Total payment=$500.00+$25.00=$525.00Total\, payment = \$500.00 + \$25.00 = \$525.00
The total payment required to pay off the promissory note is $525.00.

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