Business Mathematics Chapter 10 - Simple Interest

Given interest of $11,900 at 6% for 50 days (ordinary interest), one can calculate the principal as:

$1,428,000.00

Given interest of $11,900 at 6% for 50 days (ordinary interest), one can calculate the principal as

$11,900 / (.06 x 50/360) $11,900/ .00833 P= $1,428,000

Sandra Gloy borrowed $5,000 on a 120-day 5% note. Sandra paid $500 toward the note on day 40. On day 90 she paid an additional $500. Using the U.S. Rule, her adjusted balance after the first payment is:

$4,527.78

In calculating interest in the U.S. Rule from the last partial payment, the interest is subtracted from the adjusted balance.

False

What are the steps in making a partial payment of a loan before the due date?

1. Calculate interest on principal from date of loan to date of first principal payment. Round to nearest cent. I = P x R x T 2. Apply partial payment to interest due. Subtract remainder of payment from principal. This is the adjusted balance. 3. Calculate interest on adjusted balance that starts from previous payment date and goes to new payment date. 4. At maturity, calculate interest from last partial payment. Add this interest to adjusted balance.

Joe Flynn visits his local bank to see how long it will take for $1,200 to amount to $2,100 at a simple interest rate of 7%. The time is (round time in years to nearest tenth):

10.7 years

A note dated August 18 and due on March 9 runs for exactly:

203 days

A note dated Dec. 13 and due July 5 runs for exactly:

204 days

Simple interest loans are usually more than one year.

False

On April 5, 2015, Janeen Camoct took out an 8 1/2% loan for $20,000. The loan is due March 9, 2016. Janeen's terms are ordinary interest. Sabrina Bowers took out the same loan as Janeen. Sabrina's terms, however, are exact interest. (Use Days in a year table.)

April 5: 95th day of year 2015 March 9: 68th day of year 2016 365 - 95 = 270 270 + 68 = 338 days a. What is Sabrina's difference in interest? Ordinary Interest: 20,000 x .085 x 338/360 1,596.11 Exact Interest: 20,000 x .085 x 338/365 1,574.25 1,596.11 - 1,574.25 21.86 b. What will she pay on March 9, 2016? (Ignore leap year.) 20,000 + 1574.25 = $21,574.25

On April 5, 2015, Janeen Camoct took out an 8 1/2% loan for $20,000. The loan is due March 9, 2016. Use ordinary interest to calculate the interest. What total amount will Janeen pay on March 9, 2016? (Ignore leap year.)

April 5: 95th day of year 2015 March 9th: 68th day of year 2016 365 - 95 = 270 270 + 68 = 338 I= P x R x T I= $20,000 x .085 x 338/360 I= $20,000 x .085 x 0.94 I= $1,596.11 $20,000 + $1,596.11 = $21,1596.11

Ordinary Interest Method (360 Days)

Calculating Simple Interest using 360 days per year in time. Time = Exact Number of Days -------------------------- 360 Since banks commonly use the ordinary interest method, it is known as the bankers rule.

What is the formula for finding Principal?

Interest ------------ rate x time

Simple Interest Formula

Interest = Principal x Rate x Time Principal = Interest / Rate x Time Rate = Interest / Principal x Time Time = Interest / Principal x Rate

The U.S. rule states that when a partial payment is made, first the _____________ is covered, then the balance goes to reduce the loan ___________.

Interest, Principal

On May 3, 2014, Leven Corp. negotiated a short-term loan of $685,000. The loan is due October 1, 2014, and carries a 6.86% interest rate. Use ordinary interest to calculate the interest. What is the total amount Leven would pay on the maturity date?

May 3 = 123rd day of year Oct. 1 = 274th day of year 274 - 123 = 151 I = P x R x T I = $685,000 x 6.86% x 151/360 I = $46,991 x 151/360 I = $19,710.11 $685,000 + $19,710.11= $704,710.11

On September 12, Jody Jansen went to Sunshine Bank to borrow $2,300 at 9% interest. Jody plans to repay the loan on January 27. Assume the loan is on ordinary interest. a. What interest will Jody owe on January 27? b. What is the total amount Jody must repay at maturity?

Ordinary Interest = 360 day year a. What interest will Jody owe on January 27? Days in Year one: September 12 is the 255 day of the year. January 27th is the 27th day of the year. 365 - 255 = 110 110 + 27 = 137 I = P x R x T I = $2,300 x 0.09 x 137/360 days I = $207 x .38 I = $78.78 Interest Jody will owe on January 27: $78.78 b. what is the total amount Jody must repay at maturity? $2,300 + $78.78 = $2,378.78

On September 14, Jennifer Rick went to Park Bank to borrow $2,500 at 11¾ % interest. Jennifer plans to repay the loan on January 27. Steven Linden met Jennifer Rick at Park Bank and suggested she consider the loan on exact interest. Calculate the loan for Jennifer under this assumption.

Ordinary interest: $2500 at 11 ¾% interest from Sep 14 - Jan 27. Calculate number of days of the loan. Chart of days shows Sep 14 = day 257 of the year. 365 - 257 = 108 days to the end of the year. Add the 27 days of January to get the total days of her loan: 108 + 27 = 135 day loan $2500 x .1175 x 135/360 = $110.16 ordinary interest $2500 principal + $110.16 interest = $2610.16 total loan payoff with ordinary interest Exact interest: $2500 x .1175 x 135/365 = $ 108.65 $2500 principal + $108.65 interest = $2608.65 total loan payoff with exact interest

Martina borrowed $10,000 for 100 days. At the end of the term, she paid back $11,000

Principal: $10,000 Time: 100/360 Interest Amount: Subtract the principal from the maturity value. $11000 - $10000= $1000 Interest Rate: $1,000 ------------ = 36% $10,000 x 100/360

Kalee borrowed $10,000 for 3 months at a 4%. Match the amounts to the terms.

Principal: $10,000 Time: 3 Months Rate: 4% Interest: $100 Principal x Rate x Time 10,000 x .04 x 3/12 = $100 Maturity Value: $10,100 The principal plus the interest.

Karen borrowed $13,000 from Scott at 3.5% for 287 days. Using the exact-days method, How much is the interest for the loan?

Principal: $13,000 Interest Rate: 3.5% or .035 Exact Time 287 days Convert the number of days into an equivalent number of years: 287 287 days = ------- = .7863 365 Interest = 13,000 ( .035) (.7863) Interest = 357.77

Justin borrowed $20,000 and paid back $22,000. Match the amounts to the terms.

Principal: $20,000 Interest: $2,000 Maturity Value: $22,000

Andres Michael bought a new boat. He took out a loan for $24,500 at 4.5% interest for 2 years. He made a $4,500 partial payment at 2 months and another partial payment of $3,000 at 6 months. How much is due at maturity?

Principal: $24,500 Rate: 4.5% Time: 2 Years Partial Payment of $4,500 at 2 months I = $24,500 x 4.5% x 2/12 $1,102.50 x 0.1667 $183.75 $4,500 (Partial Payment) - $183.75 (Interest) ---------------------- = $4,316.25 (Principal Payment) Partial Payment of $3000 at 6 months:: $24,500 - $4,316.25 = $20,183.75 (Adjusted Balance) I = $20,183.75 x 4.5% x 4/12 $908.27 x .33 $302.76 $3,000 - $302.76 ----------------- = $2,697.24 Adjusted Balance: $20,183.75 - $2,697.24 = $17,486.51 How much is due at maturity:: $17,486.51 x 4.5% x 18/12 $786.89 x 18/12 $1,180.34 $1,180 + $17486.51 = $18666.85

Rosebud Mbela borrowed $400 at 5% for 28 days. Match the amounts to the terms (use exact interest)

Principal: $400 Interest Rate: 5% Time of the loan: 28 days / 365 The Interest is found by multiplying principal, rate, and time. $400 x .05 x 28/365 $400 x .05 x .0767 = $1.53 The maturity value is found by adding principal plus interest. $400 + $1.53 = $401.53

Jacob borrowed $75,000 at 18%. The loan cost $9,000. Match the items to the respective terms (use ordinary interest).

Principal: $75,000 Time Formula: Interest -------------- Principal x Rate Time in Days: $9,000 ----------- = 240 days $75,000 x .18 Maturity value: $75000 + $9000 = $84,000

Evander Holyfield (known as the man who had part of his ear bit off by Mike Tyson) made $250 million during his boxing career but declared bankruptcy due to poor financial choices. His July interest at 15% was $155. What was Evander's principal at the beginning of July? (Use 360 days a year. Do not round intermediate calculations.)

Principal= Interest/ (Rate X Time) July has 31 days 155 / 15% x 31/360 155 / .15 x .0861 155 / .012917 11,999.69

Carol Miller went to Europe and forgot to pay her $740 mortgage payment on her New Hampshire ski house. For her 59 days overdue on her payment, the bank charged her a penalty of $15. What was the rate of interest charged by the bank? (Use 360 days a year. Do not round your intermediate calculations. Round your answer to the nearest hundredth percent.)

Rate = Interest / Principal x Time $15 ---------------- = 12.37% $740 x (59/360)

Exact Interest (365 Days)

The Federal Reserve banks and the federal government use the exact interest method. The exact interest is calculated by using a 365-day year. For time, we count the exact number of days in the month that the borrower has the loan.

Lane French had a bad credit rating and went to a local cash center. He took out a $100 loan payable in two weeks at $115. What is the percent of interest paid on this loan?

There are 26 bi-weekly periods in a 365 day year. Principal: 100 Interest: 15 15 x 26 weeks = 390 390% of interest

In the U.S. Rule, the partial payment first covers the interest and the remainder reduces the principal.

True

To convert time in days, it is necessary to multiply the time in years times 360 or 365.

True

On September 14, Jennifer Rick went to Park Bank to borrow $2,500 at 11¾% interest. Jennifer plans to repay the loan on January 27. Assume the loan is on ordinary interest.

a. What interest will Jennifer owe on January 27? Calculate number of days of the loan. Chart of days shows Sep 14 = 257th day of the year. 365 - 257 = 108 days to the end of the year. Add the 27 days of January to get the total days of her loan: 108 + 27 = 135 day loan $2500 x 11¾% x 135/360 = $2,500 x .1175 x 0.375 $110.16 Jennifer will owe $110.16 on January 27th b. What is the total amount Jennifer must repay at maturity? $2500 principal + $110.16= $2610.16

U.S. Rule

states that any partial loan payment first covers and accumulatedi nterest, and the rmainder of the payment reduces the loan principal.