Simple Interest

simpleinterest


Basics

The formula provided for Interest (aka Simple Interest) by the Mathematics Formula Sheet is straightforward, but it can be rearranged to ask questions about principal, rate, and time, too.

A question involving Interest is often a plug-in (where you end up plugging in numbers for letters).

Interest = principal × rate × time
\bf\displaystyle I=prt
I = Interest = additional amount of money owed (on a loan) or earned (on a deposit)
p = principal = original amount of money owed or deposited
r = rate = percentage charged for interest
t = time = period of time over which interest is charged


Formulas (provided by Mathematics Formula Sheet)
\bf\displaystyle I=prt


Formulas (NOT provided by Mathematics Formula Sheet)

\bf\displaystyle p=\frac{I}{rt}

\bf\displaystyle r=\frac{I}{pt}

\bf\displaystyle t=\frac{I}{pr}


Question
A loan of $1000.00 is taken out at a rate of 7% for two years.
How much interest is charged over this time?

Answer
$140.00

Answer Process
\bf\displaystyle I=prt
I = 1000 × 7% × 2 = 140

Calculator Click What You See Comment
clear blinker clears screen
1000 × 7 2nd % × 2 1000*7%*2 \bf\displaystyle I=prt
enter 140 Answer
Simple Interest


Question
$5000.00 is deposited in a bank at a rate of 3% for six years.
How much interest is earned over this time?

Answer
$900.00

Answer Process
\bf\displaystyle I=prt
I = 5000 × 3% × 6 = 900

Calculator Click What You See Comment
clear blinker clears screen
5000 × 3 2nd % × 6 5000*3%*6 \bf\displaystyle I=prt
enter 900 Answer
Simple Interest


Question

$105.00 in interest was earned on a 5-year certificate of deposit at a rate of 3%.
What was the initial deposit?

Answer
$700.00

Answer Process
\bf\displaystyle p=\frac{I}{rt}

p = \bf\displaystyle\frac{\text{105}}{\text{3\%*5}} = 700

Calculator Click What You See Comment
clear blinker clears screen
fraction 105 down
2nd % × 5 right
\bf\displaystyle\frac{\text{105}}{\text{3\%*5}} \bf\displaystyle p=\frac{I}{rt}
enter 700 Answer
Simple Interest


Question

$310.00 in interest was earned on a 5-year certificate of deposit with an initial deposit of $4000.00.  What was the interest rate in decimal terms?

Answer
0.0155

Answer Process
\bf\displaystyle r=\frac{I}{pt}

r = \bf\displaystyle\frac{\text{310}}{\text{4000*5}} = 0.0155

Calculator Click What You See Comment
clear blinker clears screen
fraction 310 down
4000 × 5 right
\bf\displaystyle\frac{\text{310}}{\text{4000*5}} \bf\displaystyle r=\frac{I}{pt}
enter 0.0155 Answer
Simple Interest


Question
With reference to the above question, what was the interest rate in percent terms?

Answer
1.55%

Answer Process
See Percent.
To convert a decimal to percent, move the decimal point two places to the right.
0.0155 = 1.55%


Question

$320.00 in interest was earned on an initial deposit of $2000.00 at a rate of 4%.
How long was the money earning interest?

Answer
4 years

Answer Process
\bf\displaystyle t=\frac{I}{pr}

t = \bf\displaystyle\frac{\text{320}}{\text{2000*4\%}} = 4

Calculator Click What You See Comment
clear blinker clears screen
fraction 320 down
2000 × 4 2nd % right
\bf\displaystyle\frac{\text{320}}{\text{2000*4\%}} \bf\displaystyle t=\frac{I}{pr}
enter 4 Answer
Simple Interest


Practice – Questions

1.  What is the interest owed on a car loan of $25000.00 at a rate of 3% for five years?

2.  What is the interest owed on a credit card balance of $5000.00 at a rate of 20% for five years?

3.  $215.00 in interest was earned on a 4-year certificate of deposit at a rate of 5%.
What was the initial deposit?

4.  $3122.00 in interest was paid on a credit card balance of $4000.00 over five years.
What was the interest rate in percent terms?

5.  $800.00 in interest was earned on an initial deposit of $2000.00 at a rate of 5%.
How long was the money earning interest?


Practice – Answers

1.  $3750.00

2.  $5000.00

3.  $1075.00

4.  15.61%

5.  8 years

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