Unit 4 Seminar: Simple Interest

Define Simple Interest Formula

Compute simple interest using formula

Compute Maturity Value of an investment or loan

Ordinary interest vs. Exact Interest

Adjusted Maturity Value – Early Payment

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Interest: an amount paid or earned for the use of money.

Simple interest: interest earned when a loan or investment is repaid in a lump sum. Principal: the amount of money

borrowed or invested. Rate: the percent of the principal paid as

interest per time period. Time: the number of days, months or

years that the money is borrowed or invested.

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Shows how interest, rate, and time are related and gives us a way of finding one of these values if the other three values are known.

I = P x R x TInterest = Principal x Rate x Time

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James borrowed $8500 from his parents to purchase his first car. He agreed to pay them 6.5% simple interest per year over 5 years.

The interest is always expressed as a percentage (6.5%)

Principal is the amount borrowed or invested. ($8500) Rate of interest is a percent for a given time

period (5 years).

Be Careful! Time (T) must be expressed in the same unit of time as the rate (R).

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James borrowed $8,500 from his parents to purchase his first car. He agreed to pay them 6.5% simple interest per year over 5 years.

How much interest did James pay?

Principal = (P) $8,500 Interest = P x R x T Interest rate = 6.5% (or 0.065) = 8,500 x 0.065

x 5(When not stated assume interest rate is per year.)

Time = 5 years = $2,762.50

The interest on the loan is $2,762.506

Henry borrowed $1,200 from his parents to purchase his a dishwasher. He agreed to pay them 8% simple interest per year for 12 months.

How much interest did Henry pay?

Principal = (P) = ? Interest rate = ? Time = ? (Remember this must be in the same unit as

the rate.)Interest = P x R x T

The interest on the loan is ?

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Henry borrowed $1,200 from his parents to purchase his a dishwasher. He agreed to pay them 8% simple interest for 12 months.

How much interest did Henry pay?

Principal = (P) $1,200 Interest = P x R x T Interest rate = 8% (or 0.08) = 1,200

x 0.08 x 1 Time = 12 months = 1 year = $96

The interest on the loan is $96

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Maturity value: the total amount of money due by the end of a loan or investment period - includes the principal and interest

Maturity Value of Loan = Principal + Interest

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MV = principal + interest

But interest = I = P*R*T So, MV = principal + PRT This is the same as MV = P + PRT We can factor out the P to get MV = P(1+RT)

Remember to multiply R*T before adding 1.

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Marcus Logan can purchase furniture on a 2-year simple interest loan at 9% interest per year.

What is the maturity value for a $2,500 loan?

MV = P (1 + RT) Verify time units match. Substitute known values. MV = $2,500 [ 1 + (0.09 x 2)] MV = $2,500 [ 1 + 0.18 ] MV = $2,500 [ 1.18 ] MV = $2,950

This is what Marcus will owe at the end of the two years.

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Terry Williams is going to borrow $4,000 at 7.5% annual simple interest. What is the maturity value of the loan after three years?

MV = P [ 1 + (R*T)]

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MV = P [ 1 + (R*T)] P = $4,000 R = 7.5% per year T = 3 years

MV = $4,000 [ 1 + (0.075*3)]= $4,000 [ 1 + 0.225 ] = $4,000 [ 1.225]= $4,900

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What if we are faced with this problem?

To save money, Stan Wright invested $2,500 for 42 months at 4 ½ % simple interest. How much interest did he earn?

How do we calculate the problem when we have a weird number of months?

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Write the number of months as the numerator of a fraction.

Write 12 as the denominator of the fraction because there are 12 months in a year.

Reduce the fraction to lowest terms if using the fractional equivalent.

Divide the numerator by the denominator to get the decimal equivalent of the fraction

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CONVERT 9 MONTHS AND 15 MONTHS, RESPECTIVELY, TO YEARS, EXPRESSING BOTH AS FRACTIONS AND DECIMALS

9/12 = ¾ = 0.75

9 months = 0.75 of a year

15/12 = 1 3/12 = 1 ¼ = 1.25

15 months = 1.25 of years

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To save money, Stan Wright invested $2,500 for 42 months at 4 ½ % simple interest. How much interest did he earn?

First convert the time to the same units.

42 months = 42/12 = 3.5 years Convert the interest rate to a decimal.

4 ½% = 4.5% Divide by 100 to get 0.045 Then substitute known values into our formula I = PRT.

I = $2,500 x 0.045 x 3.5 = $393.75

Stan will earn $393.75 in interest

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We can find any of the 4 values if we know the other three …

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I = PRT Use formula operations to solve for P

P = I / RT

Judy paid $108 in interest on a loan that she had for 6 months. The interest rate was 12%. How much was the principal?

P = 108/ (0.12 x 0.5) We converted 6 months to 0.5 years

P = 108/0.06

P = $1,800

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I = P R T Use formula operations to solve for R R = I / PT

Sam wants to borrow $1,500 for 15 months and will have to pay $225 in interest. What rate is charged?

Rate = $225/ ($1,500 x 1.25) 15 months = 1.25 years

R = 225/1,875 R = .12 or 12%

The rate Sam will pay is 12%. 20

I = P R T Use formula operations to solve for T

T = I / RP

Shelby borrowed $10,000 at 8% and paid $1,600 in interest. What was the length of the loan?

Time = $1,600/(0.08 x $10,00o)

T= $1,600/800

The loan period was 2 years

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Ordinary time: time that is based on counting 30 days in each month.

30 days per month * 12 months a year = 360 days in a year.

Exact time: time that is based on counting the exact number of days in a time period.

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The ordinary time from July 12 to September 12 is 60 days.

July 12 to August 12 = 30 daysAugust 12 to Sept. 12 = 30 days

To find the exact time from July 12 to September 12, add the following:

Days in July (31 - 12 = 19)

Days in August: 31Days in Sept. + 12

19 + 31 + 12 = 62 days

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Subtract the beginning date’s sequential number from the due date’s sequential number.

What is the exact time between May 5th and August 5th?

On the table Aug 5 = 217 and May 5 = 125 217-125 = 92 days is the exact time

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1. Subtract the beginning date’s sequential number from 365.

(With 365 days in a year, how many are left that we need?)

2. Add the due date’s sequential number to the result from the previous step.

(Now add in how many days in this year we will use.)

3. If February 29 falls between the two dates, add 1.

(Having 2/29 makes it a leap year, so we have 366 days in that year.)

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Find the exact time from May 15 on Year 1 to March 15 in Year 2.

Step 1: May 15 is day 135365 – 135 = 230

Step 2: March 15 is day 74230 + 74 = 304 days

The exact time is 304 days.

Note: If Year 2 is a leap year, the exact time is 305 days.

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A loan made on September 5 is due July 5 of the following year.

Find: a) ordinary time b) exact time in a non-leap

year c) exact time in a leap year.

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A loan made on September 5 is due July 5 of the following year.

a. Ordinary time = 300 daysCount the months, 10 between Sept and July. Ordinary assumes 30 days per month. 30 * 10 = 300 days.

b.Exact time (non-leap year) = 303 daysGet the days remaining in the first year. 365 – Sept.5 = XLook up the days used in the next year. Value for July 5 = Y Add those together = X + Y = 303

c. Exact time (leap year) = 304 daysWe know exact time with out a leap year is 303. We also know that July 5th is after February 29th which means there is an extra day unaccounted for. 303 + 1 = 304 days.

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Ordinary interest: a rate per day that assumes 360 days per year.

Exact interest: a rate per day that assumes 365 days per year

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A loan for $500 was made on March 15 and due on May 15. The annual interest rate is 7%.

Length of loan (ordinary time) =

30 days * 2 months = 60 days

Using ordinary time, we want 60 days of 360 in a year.

Rate = 0.07 for the year Interest = PRT = $500 * 0.07 * (60/360) Interest = $5.83

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A loan for $500 was made on March 15 and due on May 15. The annual interest rate is 7%.

Length of loan (exact time) = 61 days {Use the table}

Using exact time, we want 61 days of an ordinary year or 360.

Rate = 0.07 Interest = $500 * 0.07 * (61/360) Interest = $5.93

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A loan for $500 was made on March 15 and due on May 15. The annual interest rate is 7%.

Length of loan (exact time) = 61 days

Using exact time, we want 61 days of an exact year or 365.

Rate = 0.07 Interest = $500 * 0.07 * (61/365) Interest = $5.84

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Time Rate Interest

Ordinary interest using ordinary time

60 days

7% $5.83

Ordinary interest using exact time

61 days

7% $5.93(highest)

Exact Interest using exact time

61 days

7% $5.84

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Financial institutions typically calculate interest on a loan based on ordinary interest and exact time

…. which yields a slightly higher amount of interest.

This is because you get a higher per day interest rate dividing by 360 instead of 365 and you use it over the exact days rather than only 30 days in a month.

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Tony borrows $5,000 on a 10%, 90 day note. On the 30th day, Tony pays $1,500 on the note. If ordinary interest is applied using exact time (banker’s rule), what is Tony’s adjusted principal after the partial payment, and adjusted balance due at maturity?

We split the loan length into two periods – before the partial payment and after.

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1. Determine the exact time from the date of the loan to the first partial payment.

2. Calculate the interest for period up to the payment. Subtract that interest from the partial payment.

3. Reduce the initial Principal by the remaining amount of the partial payment. This is the adjusted principal.

4. At maturity, calculate interest from the last partial payment and add to adjusted principal. This is the adjusted balance due at maturity.

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Tony borrows $5,000 on a 10%, 90 day note. On the 30th day, Tony pays $1,500 on the note. If ordinary interest/exact time is applied, what is Tony’s adjusted principal after the partial payment, and adjusted balance due at maturity?

1. Determine the exact time from the date of the loan to the first partial payment.

▪ 30th Day. Using ordinary interest, our time for interest will be 30/360.

2. Calculate the interest for period up to the payment.▪ I = PRT▪ I = $5,000(.1)(30/360) = $41.67

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Tony borrows $5,000 on a 10%, 90 day note. On the 30th day, Tony pays $1,500 on the note. If ordinary interest is applied, what is Tony’s adjusted principal after the partial payment, and adjusted balance due at maturity?

3. Reduce the initial Principal by the amount of the partial payment. This is the adjusted principal.

▪ The interest we calculated was $41.67. ▪ We pay the interest off first. So reduce your partial

payment by the interest. P – I = $1,500 - $41.67 = $1,458.33

▪ Then you subtract the rest of the partial payment to reduce the principal. $5,000 - $1,458.33 = $3,541.67 This is the adjusted principal, the amount you will calculate interest on in the future.

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Tony borrows $5,000 on a 10%, 90 day note. On the 30th day, Tony pays $1,500 on the note. If ordinary interest is applied, what is Tony’s adjusted principal after the partial payment, and adjusted balance due at maturity?

4. At maturity, calculate interest from the last partial payment and add to adjusted principal. This is the adjusted balance due at maturity.

▪ Our new principal is $3,541.67▪ On our 90 day note, 30 days have past so we have 60

days left. Using ordinary interest our time is now 60/360.▪ Our new interest amount is now I = PRT = $3,541.67(.1)

(60/360) = $59.03 ▪ This is our new interest due so we add this to the

principal balance due on our loan. ▪ Our adjusted balance or balance due is

$3,541.67 + $59.03 = $3,600.70

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1. Determine the exact time from the date of the loan to the first partial payment.

2. Calculate the interest for period up to the payment. Subtract that interest from the partial payment.

3. Reduce the initial principal by the remaining amount of the partial payment. This is the adjusted principal.

(You could repeat the above steps for as many partial payments as you need to.)

4. At maturity, calculate interest from the last partial payment and add to the adjusted principal. This is the adjusted balance due at maturity.

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Reminder of what to complete for Unit 4: Discussion = initial

response to one question + 2 reply posts

MML assignment Instructor graded

assignment (download from doc sharing)

Seminar quiz if you did not attend, came late, or left early