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Questions and Answers
What does the total amount due at the end of a simple interest loan consist of?
What does the total amount due at the end of a simple interest loan consist of?
- The capital only
- The interest only
- The principal plus the interest (correct)
- The interest minus any fees
Which formula correctly calculates the simple interest earned on an investment?
Which formula correctly calculates the simple interest earned on an investment?
- I = (S - P) / t
- I = P(1 + rt)
- I = P + rt
- I = Prt (correct)
What is the accumulation factor at simple interest referred to as?
What is the accumulation factor at simple interest referred to as?
- Interest factor
- Discount factor
- Financing factor
- Accumulation factor (correct)
If the principal amount is $1000, the rate of interest is 5% per year, and the time period is 3 years, how much interest will be earned?
If the principal amount is $1000, the rate of interest is 5% per year, and the time period is 3 years, how much interest will be earned?
Which statement about the discounted present value is accurate?
Which statement about the discounted present value is accurate?
In the context of simple interest, what is meant by the term 'principal'?
In the context of simple interest, what is meant by the term 'principal'?
Which of the following statements is NOT true about simple interest?
Which of the following statements is NOT true about simple interest?
How is the maturity value calculated in a simple interest situation?
How is the maturity value calculated in a simple interest situation?
What formula is used to find the ordinary simple interest on a 60-day loan based on a 360-day year?
What formula is used to find the ordinary simple interest on a 60-day loan based on a 360-day year?
How many days are used as the basis for calculating ordinary simple interest in international business transactions?
How many days are used as the basis for calculating ordinary simple interest in international business transactions?
If $1200 is lent at a simple interest rate of 12% for 6 months, what is the interest earned?
If $1200 is lent at a simple interest rate of 12% for 6 months, what is the interest earned?
How is simple interest calculated over a 365-day year based on the formula provided?
How is simple interest calculated over a 365-day year based on the formula provided?
What total amount must be repaid after borrowing $1000 for 220 days at an interest rate of 12.17%?
What total amount must be repaid after borrowing $1000 for 220 days at an interest rate of 12.17%?
What is the duration in days it will take for $8500 to accumulate at least $550 at a 13% ordinary simple interest rate?
What is the duration in days it will take for $8500 to accumulate at least $550 at a 13% ordinary simple interest rate?
When calculating the exact simple interest based on a 365-day year, which of the following is considered?
When calculating the exact simple interest based on a 365-day year, which of the following is considered?
What is the principal amount if a borrower pays back $850 after 80 days with a simple interest rate of 90%?
What is the principal amount if a borrower pays back $850 after 80 days with a simple interest rate of 90%?
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Study Notes
Simple Interest Overview
- Simple interest is calculated based only on the original principal amount borrowed.
- The borrower repays the principal plus the interest charged for its use, termed as income for the investor.
- The initial amount invested is referred to as the principal.
Key Terms and Formulas
- Principal (P): The original amount of money lent or invested.
- Interest (I): The cost of borrowing money, calculated as I = Prt, where:
- r = annual rate of interest
- t = time in years
- Accumulated Value (S): The total amount to be repaid, given by S = P + I = P(1 + rt).
- Accumulation Factor: The term (1 + rt) is used to calculate the accumulated value.
- Discount Factor: P can be calculated using S and the formula P = S / (1 + rt).
Time Considerations
- Time (t) must be expressed in years.
- For months, t = number of months / 12.
- For days, t = number of days / 365 or based on a 360-day year for ordinary simple interest.
Ordinary Simple Interest
- Ordinary simple interest often uses a 360-day year instead of a 365-day year, which can affect interest calculations.
- Common in the United States and international transactions.
Example Calculations
- For a 60-day loan of $1500 at 14.5%, the ordinary interest calculation involves:
- I = 1500 * (0.145) * (60/360) = $36.25
- Using 365 days yields a different amount depending on the specific term used.
Problem Solving
- To find the rate of simple interest that allows $1200 to accumulate $72 in 6 months:
- r = Interest / (Principal * Time) = 72 / (1200 * (1/2)) = 0.12 or 12%.
- To determine the time it takes for $8500 to accumulate at least $550 at 13% interest:
- t = Interest / (Principal * Rate) = 550 / (8500 * 0.13) = Approximately 226.04 days.
- For a $1000 loan for 220 days at 12.17%, the repayment amount can be calculated:
- S = 1000 * [1 + (0.1217)(220/360)] = $1,074.37.
- If an individual repays $850 after borrowing, the principal can be derived using:
- P = S * [1 + (0.4975)(81/360)]^(-1) = $31.97.
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