Simple Interest

Example 1: Jamie deposited $900 in his bank account and waited for 2 years. Find the account balance if the interest rate offered by the bank is 7%.

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Solution:

To find the bank balance at the end of 2 years, calculate the simple interest and add it to the principal.聽

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I = Prt

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\(I=900\times 0.07\times 2\)

聽 \(=9\times 7\times 2\)

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聽 = $126

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So, simple interest is $126

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Bank balance = Principal amount + simple interest

聽 聽 聽 聽 聽 聽 聽 聽 聽 聽 聽 聽= $900 + $126

聽 聽 聽 聽 聽 聽 聽 聽 聽 聽 聽 聽= $1026聽

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Example 2: Bella borrowed $15,000 to buy a car. If she has to pay a total simple interest of $3000 at the end of 5 years, find the rate of interest at which she took the loan.聽

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We can find the rate of interest by rearranging the terms in the simple interest equation.聽

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I = Prt

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\(r=\frac{I}{Pt}\)

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聽 \(=\frac{3000}{15,000\times 5}\)

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聽 \(=\frac{3}{15\times 5}\)

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聽 \(=\frac{1}{5\times 5}\)

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聽 \(=\frac{1}{25}=0.04\times 100=4\)%

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Therefore, Bella borrowed the money at a rate of interest of 4% per annum.聽

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Example 3: Joshua deposited $8000 in a bank at a rate of 6% per annum. Find the time period in which the interest will add up to $2400.聽

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Solution:

Principal amount = $8000

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Simple interest = $2400

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Rate of interest \(=6\)% = \(\frac{6}{100}=0.06\)

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I = Prt

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\(t=\frac{I}{Pr}\)

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\(=\frac{2400}{8000\times 0.06}\)

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\(=\frac{240}{8\times 6}\)

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\(=\frac{240}{48}=5~\text{years}\)

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Therefore, it will take 5 years for the interest to add up to $2400.

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Example 4: The yearly balance of a bank account is given in the table. What is the interest rate of the account? Find the bank balance after 15 years.聽

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Solution:

The balance is the amount we get after adding the interest to the principal. So if no interest has been incurred, that is if the principal has not even completed a year of deposit, then the balance is simply the principal itself.聽

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Hence initially (when year = 0), the principal = balance = $1200.

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So, Principal P = $1200

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The account balance after 1 year is $1332.聽

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Balance amount = Principal amount + Simple interest

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Simple interest = Balance amount – Principal amount

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I = $1332 – $1200 = $132

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So, the interest at the end of the first year is $132.聽

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We can find the rate of interest from the information available to us.

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I = Prt

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\(r=\frac{I}{Pt}\)

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\(=\frac{132}{1200\times 1}=0.11\times 100=11\)%

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Therefore, the rate of interest is 11%.聽

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Now, we can find the account balance at the end of 15 years.聽

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I = Prt

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聽 \(=1200\times 0.11\times 15\)

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聽 = $1980

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Therefore, the simple interest earned in 15 years is $1980.

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Balance amount = Principal amount + Simple interest

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In Simple interest calculations, the principal remains constant.聽

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Balance amount = $1200 + $1980 = $3180

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So, the account balance after 15 years will be $3180.