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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

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

Answer (c) is the correct answer

$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

Answer (c) is the correct answer

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

Answer (a) is the correct answer

$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

Answer (a) is the correct answer

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

Answer (a) is the correct answer

$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

Answer (a) is the correct answer

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

Answer (b) is the correct answer

$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

Answer (b) is the correct answer

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

Answer (d) is the correct answer

$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

Answer (d) is the correct answer

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

Answer (a) is the correct answer

$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

Answer (a) is the correct answer

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

Answer (b) is the correct answer

$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

Answer (b) is the correct answer

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

Answer (d) is the correct answer

$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

Answer (d) is the correct answer

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

Answer (c) is the correct answer

$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

Answer (c) is the correct answer

$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

Answer (b) is the correct answer