Some people keep money at home in an easily accessible location, perhaps a piggy bank, a safe or locked box, or perhaps even a mattress. Although this provides instant access to funds it does not provide any return or earnings on this money. For that reason, most people hold their money in accounts or investments that provide some form of return or earning power. Show Interest is the price paid for the use of money. If you borrow money from another person or a lending institution, eventually you must pay back this amount plus the interest owing. When you deposit money in a bank, you are lending them money and after some time they will pay you interest on the money you lent them. The amount of interest you will owe or receive is determined by the principal, the interest rate, and the time (the length of the loan). The amount of money that you lend or borrow is called the principal. The length of the loan can range between a few days to several years. The interest rate is stated as an annual percentage. It may be simple interest or compound interest. With simple interest the interest is calculated only once during the entire time period of the loan or deposit. Simple interest is calculated solely on the principal investment or loan. With compound interest the interest is calculated more than once during the time period of the loan. It will be calculated on the principal as well as the accumulated interest This section will focus on simple interest and in the next section we will consider compound interest. Simple interest is calculated by finding the product of the principal (P), the rate (r), and the time (t). The simple interest formula is I = Prt where I = interest earned r = annual interest rate ( stated as a decimal) P = principal t = time (in years) Interest rates are quoted for periods of one year and when used in a formula must be converted to a decimal fraction. The time must be expressed in the same unit of time as the interest rate so time must be stated in years or portions of a year. If you deposit money in a savings account earning 3% interest then the annual interest rate is 3% per year. Jo borrows $2000 at an interest rate of 5% per year. How much interest will Jo owe after one year? Solution Identify the P, r, and t. P = $2000 r = 5% = 0.05 t = 1 year Here,Replace P, r and t with their valuesChange 5% to its decimal equivalent, 0.05Start with the formula I = Prt I = 2000 (5%) (1) Replace P, r, and t with their values I = 2000 (0.05) (1) Change 5% to its decimal equivalent, 0.05 I = 100 Jo will pay $100 in interest. Terri borrowed $3200 at an interest rate of 4.75%. How much interest will Terri owe on the loan at the end of one year? Show answer
Note that the time t is expressed in terms of years. When the time period is not exactly one year, the value for t will be the fraction of the year during which interest is earned. If the investment is made for 3 months, then t = 3 months/12 months = 0.25 years. If the investment is made for 35 days then t = 35 days/365 days = 7/73 years. a) If an investment is made for a period of 145 days, what portion of the year does this represent? b) If an investment is made for a period of 48 weeks, what portion of the year does this represent? c) If an investment is made for a period of 10 months, what portion of the year does this represent? Solution: a) 145 ÷ 365= 29/73 years b) 48 ÷ 52 = 12/13 years c) 10 ÷ 12 = 5/6 years a) If an investment is made for a period of 220 days, what portion of the year does this represent? b) If an investment is made for a period of 32 weeks, what portion of the year does this represent? c) If an investment is made for a period of 2 months, what portion of the year does this represent? Show answera) 220 ÷ 365= 44/73 year b) 32 ÷ 52 = 8/13 year c) 2 ÷ 12 = 1/6 year Determine the interest that will be earned on a deposit of $1350 at 2.8% over: a) 7 months b) 25 days Solution: a) Interest of $22.05 over 7 months b) Interest of $2.59 over 25 days. Note that the answer is rounded to the nearest two decimal places or to the nearest cent. Determine the interest that will be earned on a deposit of $2200 at 4.52% over: Determine the interest earned after a) 1 month b) 300 days Show answera) $8.29 b) $81.73 Determine the interest that will be earned on a deposit of $4200 at 4.65% over: a)years b) 5 weeks Solution a) Interest of $292.95 overyears b) Interest of $18.78 over 5 weeks. Note that the answer is rounded to the nearest two decimal places or to the nearest cent. Max deposited $1500 in a savings account at an interest rate of 3.28%. Determine the interest earned after i) 3 months ii) 65 days iii) two years. Show answerThe total amount of money due at the end of a loan period is called the maturity value of the loan. It is the amount to be paid on the due date of a loan or the amount to be paid to an investor at the end of the period for which an investment has been made. The Maturity Value (MV) of a loan is the sum of the principal P plus the interest I. MV = P + I In Example 1, Jo borrowed $2000 at an interest rate of 5%. At the end of one year Jo owed $100 in interest. The maturity value of the loan is MV = P + I where P = $2000 and I = $100. MV = $2000 + $100 = $2100 The maturity value of the loan is $2100. At the end of the year Jo will be expected to pay back $2100. Linda lends Ed $500. Ed says he will pay her back in 60 days at 9% simple interest. How much interest should Linda receive? How much must Ed pay Linda altogether? Solution Replace P, r and t with their valuesMultiplyRound to the nearest centMV = P + I = $500 + $7.40 = $507.40 Linda should receive $7.40 in interest. At the end of 60 days Ed will owe Linda $507.40. In order to purchase equipment, a barbershop takes out a short term loan of $3000 at a rate of 4.35%. The loan is due in 80 days. Determine the interest that will be owed at the end of 80 days and find the maturity value of the loan. Show answerInterest owed is $28.60, MV is $3028.60 The amount of interest earned on an investment or due on a loan is calculated using I = Prt. This formula can also be used to determine:
These amounts can be determined by solving the simple interest formula for any of r, P or t. whereTo determine the principal use:I = interest earnedTo determine the interest rate use:r = annual interest rateTo determine the time use:P = principalt = time (in years) The following memory aid is often called the “Magic Triangle”, because if you cover the variable you are trying to find, the formula will magically appear! A six month investment will earn 5.25%. How much would you need to invest if you want to earn $100 in interest? Solution The principal is unknown. Cover P in the Magic Triangle. P = ? or appears. Use the formula:or Replace I, r and t with their respective values Multiply 0.0525 by 0.5 Divide 100 by 0.02625 and round answer to nearest centYou would need to invest $3809.52 A student borrowed money from his best friend at the very low interest rate of 1.5% for a period of 9 months. At the end of 9 months the friend had earned $22.50 in interest. Determine the original amount of the loan. Show answerMariko had $240 in the bank for the month of April. At the end of the month she had earned $0.90 in interest. What interest rate was the bank paying? Solution The interest rate is unknown. Cover r in the Magic Triangle. r = ? or appears. Use the formula:Since r = 0.045, the interest rate as a percentage is 4.5% Kris deposited $800 in an account. At the end of 6 months he had earned $10.40. Determine the interest rate. Show answerCarol invested $500 at an interest rate of 6%. How long will it take her to earn $250 in interest? Solution The time is unknown. Cover t in the Magic Triangle. t = ? or appears. UseIt will take 8.33 years. An account earns 4% interest. How long will it take for a deposit of $4000 to earn $240 in interest? When calculating time “t” using the simple interest formula, the answer will be in terms of years. Sometimes it is more reasonable to express the answer in terms of days or months. When converting time (in years) to months or days: To express the time in months (m): Multiply the time “t” in years x 12 months/year. If time t = 0.25 years then the number of months m = 0.25 years x 12 months/year = 3 months To express the time in days (d): Multiply the time “t” in years x 365 days/year. If time t = 0.25 years then the number of days d = 0.25 years x 365 days/year = 91.25 days Troy invested $4000 in an account offering 3.8%. How long will it take him, in days, to earn $30 in interest? Solution = Time in days = 0.1974 years x 365 days/year = 72 days It will take 72 days to earn $30 in interest Tam invested $1875 in an account offering 4%. How long will it take her, in months, to earn $62.50 in interest? Show answeryears so 0.833… years12 = 10 months
I = interest earned r = annual interest rate ( stated as a decimal) P = principal amount t = time (in years)
maturity value is the amount to be paid on the due date of a loan or the amount to be paid to an investor at the end of the period for which an investment has been made. principal is the amount of money that has been invested or borrowed. simple interest is interest that is calculated only once during the entire time period of the loan or deposit. Simple interest is calculated solely on the principal investment or loan.
Some of the content for this chapter is from “Unit 1: Simple interest” and “Unit 2: Variations on simple interest” in Financial Mathematics by Paul Grinder, Velma McKay, Kim Moshenko, and Ada Sarsiat, which is under a CC BY 4.0 Licence.. Adapted by Kim Moshenko. See the Copyright page for more information. What rate of interest will simple interest be half the principal in 5 years?Expert-verified answer
The rate of interest will simple interest be half the principal in 5 years. Assume the principal be Rs 100. Then, interest will be Rs 50. So, the rate of interest is 10%.
On what principal simple interest of 5 years at the rate of 6% is Rs?Expert-Verified Answer
Simple interest of Rs. 90 in 5 years at the rate of 6%.
What is the interest of rupees 500 in 5 years at the rate of 5% simple interest per annum?500 at the rate of 5% is Rs. 100.
In what time will the simple interest be 2 5?The simple interest be 2/5 of the principal at 8 percent per annum. ∴ The time is 5 years.
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