5/26/2008
Personal Loans and Simple Interest
“To Buy or NOT to Buy”, that is the question.
Often consumers want to buy clothing, appliances, cars, boats, and/or houses, but they do not have the cash to purchase the item So, the consumer is faced with a challenge: “Should I borrow the money and pay the interest or can I WAIT until I can pay cash?” If the consumer decides the item cannot wait, he/she faces applying for credit and paying interest.
Personal loans
• The amount of credit and the interest that a consumer may obtain depends on the assurance that he/she can give the lender that he/she will be able to repay the loan. • Security ( ll i (collateral) is anything of value pledged l) i hi f l l d d by the borrower that the lender may sell or keep if the borrower does not repay the loan. • A personal noteis a document that states the terms and conditions of the loan
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INTEREST…….
Interest can be beneficial and costly!! While you may not yet understand terms such as interest rate and compounded monthly ONE thing seems clear, money in certain savings accounts grow rapidly and paying off credit cards can be VERY challenging!
Define types of Interest
• Interest is the dollar amount that a person is either paid for lending money to the bank (SAVINGS acct) OR the amount of money the that must be paid to use the lender’s money. (LOAN) • Simple interestis based on the entire amount of the loan for the total period of the loan.
Calculating Simple Interest
Interest = principal × rate × time i = prt
Where time is expressed in YEARS and rate is expressed in DECIMAL form.
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Calculating Simple Interest for a Year
You deposit $2000 in a savings account at Hometown Bank, which has a rate of 6%. Find the interest at the end of the first year.
Solution
p = the amount deposited, or principal p = $2000. r = rate = 6% = 0.06. t = one year The interest is: I = Prt = ($2000)(0.06)(1) = $120. At the end of the first year, the interest is $120. You can withdraw the $120 in interest, and you still have $2000 in the savings account.
Example: Calculating Interest and Payback Amount
Lillian needs to borrow $1900 for tuition, from a credit union. She obtains a 6‐month loan with an annual simple interest rate of 5.5%. A. Calculate the simple interest on the loan. A Calculate the simple interest on the loan B. Determine the amount that Lillian will pay the credit union at the end of six months.
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Solution: Calculate the simple interest on the loan.
i = p×r ×t = $1900 × 0.055 × 0.5 = $52.25
The simple interest on $1900 at 5.5% for 6 months is $ 52.25.
Determine the amount that Lillian will pay the credit union at the end of six months.
The amount to be repaid is equal to the principle plus the interest.
A= p+i = $1900 + $52.25 = $1952.25
To pay off her loan, Lillian will need $1952.25.
Discount Notes
The discount note is a loan where the interest is paid at the time the borrower receives the loan. The interest charged in advance is called the bank discount.
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Glen Marshall borrowed $2750 on a 8% discount note for a period of 9 months
A. Find the interest that must be paid when the loan is received. B. Find the actual interest rate for the loan.
SOLUTION: This is the same thing as the Interest. Since this is a simple interest rate:
i = p×r ×t i = $2750 × 0.08 × i = $165.00 9 12
The interest that must be paid when he receives the loan is $165.00
B. Find the actual interest rate for the loan.
Calculate the actual interest rate by using the interest calculated in the previous part. (Note: the amount received or the principle is actually the amount borrowed minus the interest that was paid.)
i = p×r ×t =
$165 00 = ($2750 − 165) × r × 5.0
9 12
$165.00 = 2585 × r × $165.00 =
9 12
$ 1 6 5 .0 0 = 1 9 3 8 .7 5 × r
2585 9 × ×r 1 12
$165.00 ≈r $1938.75 0.0851 = r
The actual rate was 8.51%
The United States Rule
The United States rule states that if a partial payment is made on the loan, interest is computed on the principle from the first day of the loan until the date of the partial payment. – The partial payment is used to pay the interest first; the rest of the payment is used to reduce the principal. – The balance due on the date of maturity is found by computing interest due since the last partial payment and adding this interest to the unpaid principle.
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Banker’s Rule
• The banker’s rule is used to calculate simple interest when applying the United States rule. • The banker’s rule considers a year to have 360 days and any fractional part of a year is the exact number of days of the loan. loan
See Table 11.1 pg 607
Example
• Use Table 11.1 to find (a) the due date of a loan made on March 15 for 120 days and (b) the number of days from April 18 to July 31 Use Table 11.1 to find Day 15 in the left column (with heading Day of Month). Move 3 columns to the right (March heading) to find the red circled #74.
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continued
March 15 is the 74th day of the year. ADD 120 to 74 to find the due date of the loan. 120 + 74 = 194 120 + 74 = 194 The 194th day is July 13. The loan is due July 13
b) the number of days from April 18 to July 31
To determine the number of days from April 18 to July 31, use Table 11.1 • April 18 is the 108th day of the Banker’s calendar. • July 31st is the 212th day of the bankers calendar.
» 212‐108 = 104
• Thus the number of days from April 18 to July 31 is 104 days.
Example:
Determine the simple interest that will be paid on a $700 loan at an interest rate of 6% for the period March 16 to October 16 using the Banker’s rule. We need to find the number of days of the loan. Referring to Table11.1 on page 607 in your text book, March f bl b k h 16 is the 75thday of the year and October 16 is the 289th day of the year. ( DAYS: 289‐75 = 214) The period of time in years is 214/360. The interest is $24.97.
i = prt = $700 × 0.06 × = $24.97 214 360
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