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Business Math 03 - Calculating Interest Per Day (Practice 1)

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You have learned how to calculate simple interest per year. It is pretty straightforward in that, using the formula, it is the principal times the interest rate times the number of years (I = PRT). But what happens if the principal amount is paid off in days rather than years? Let’s look at an example problem.

You want to borrow some money for a short period of time, say \$6,300.00 at 8% for 310 days. We still use the formula I = PRT but now our worked problem should look as follows:

Working the problem:
\$6,300.00 at 8% for 310 days
(as there are 365 days in a year but you are only using the money for 310 days, you show this in a fraction, i.e., 310 days/365 days)
I = PRT
6,300 x 0.08 x 310/365
6,300 x 0.08 = 504
\$504.00 per year (but we don’t need the whole year so we must now divide as follows)
504 ÷ 365 (days) = 1.3808219 (this means the interest per day [also referred to as per diem] is \$1.3808219)
\$1.3808219 x 310 (days) = \$428.05
I = \$428.05

There are a few more steps to follow in calculating the per diem that now includes division but if you take each step slowly, you should have no problem finding the amount of interest that will be owed or paid at the end of the time period mentioned in each of the following ten problems.

1.
\$675.00 at 5.2% for 332 days.
\$39.31
\$31.93
\$13.39
\$33.91
Working the problem
\$675.00 at 5.2% for 332 days.
I = PRT
675 x 0.052 x 332/365
675 x 0.052 = 35.10
\$35.10 per year
35.10 ÷ 365 (days) = 0.0961644 per diem
\$0.0961644 x 332 (days) = \$31.93
I = \$31.93
2.
\$64,725.00 at 8% for 180 days.
\$2,553.35
\$2,355.35
\$2,553,53
\$2,535.53
Working the problem
\$64,725.00 at 8% for 180 days.
I = PRT
64,725 x 0.08 x 180/365
64,725 x 0.08 = 5,178
\$5,178.00 per year
5,178 ÷ 365 (days) = 14.1863014 per diem
\$14.1863014 x 180 (days) = \$2,553.53
I = \$2,553.53
3.
\$100.00 at 3.23% for 60 days.
\$0.53
\$5.30
\$5.03
\$0.35
Working the problem
\$100.00 at 3.23% for 60 days.
I = PRT
100 x 0.0323 x 60/365
100 x 0.0323 = 3.23
\$3.23 per year
3.23 ÷ 365 (days) = 0.0088493 per diem
\$0.0088493 x 60 (days) = \$0.53
I = \$0.53
4.
\$3,750.00 at 7.13% for 118 days.
\$86.44
\$96.44
\$76.44
\$106.44
Working the problem
\$3,750.00 at 7.13% for 118 days.
I = PRT
3,750 x 0.0713 x 118/365
3,750 x 0.0713 = 267.38
\$267.38 per year
267.38 ÷ 365 (days) = 0.7325479 per diem
\$0.7325479 x 118 (days) = \$86.44
I = \$86.44
5.
\$8,300.00 at 9.25% for 212 days.
\$454.39
\$445.93
\$445.39
\$544.93
Working the problem
\$8,300.00 at 9.25% for 212 days.
I = PRT
8,300 x 0.0925 x 212/365
8,300 x 0.0925 = 767.75
\$767.75 per year
767.75 ÷ 365 (days) = 2.1034247 per diem
\$2.1034247 x 212 (days) = \$445.93
I = \$445.93
6.
\$2,500.00 at 4.25% for 300 days.
\$106.33
\$106.26
\$78.33
\$87.33
Working the problem
\$2,500.00 at 4.25% for 300 days.
I = PRT
2,500 x 0.0425 x 300/365
2,500 x 0.0425 = 106.25
\$106.25 per year
106.25 ÷ 365 (days) = 0.2910959 per diem
\$0.2910959 x 300 (days) = \$87.33
I = \$87.33
7.
\$25,000.00 at 6.75% for 243 days.
\$1,123.46
\$1,132.46
\$1,132.64
\$1,123.64
Working the problem
\$25,000.00 at 6.75% for 243 days.
I = PRT
25,000 x 0.0675 x 243/365
25,000 x 0.0675 = 1,687.50
\$1,687.50 per year
1,687.50 ÷ 365 (days) = 4.6232877 per diem
\$4.6232877 x 243 (days) = \$1,123.46
I = \$1,123.46
8.
\$18,515.00 at 5.175% for 265 days.
\$659.46
\$695.64
\$665.94
\$645.59
Working the problem
\$18,515.00 at 5.175% for 265 days.
I = PRT
18,515 x 0.05175 x 265/365
18,515 x 0.05175 = 958.15
\$958.15 per year
958.15 ÷ 365 (days) = 2.6250685 per diem
\$2.6250685 x 265 (days) = \$695.64
I = \$695.64
9.
\$425.00 at 2.85% for 90 days.
\$2.79
\$2.97
\$2.89
\$2.99
Working the problem
\$425.00 at 2.85% for 90 days.
I = PRT
425 x 0.0285 x 90/365
425 x 0.0285 = 12.11
\$12.11 per year
12.11 ÷ 365 (days) = 0.0331849 per diem
\$0.0331849 x 90 (days) = \$2.99
I = \$2.99
10.
\$1,525.00 at 4.85% for 309 days.
\$66.12
\$61.62
\$62.61
\$61.26
Working the problem
\$1,525.00 at 4.85% for 309 days.
I = PRT
1,525 x 0.0585 x 309/365
1,525 x 0.0485 = 73.96
\$73.96 per year
73.96 ÷ 365 (days) = 0.2026301 per diem
\$0.2026301 x 309 (days) = \$62.61
I = \$62.61