# INTEREST WORD PROBLEMS

Investment and interest word problems usually involve simple interest using the formula given below.

I = PRT

Here,

I  =  Interest on the original investment

R  =  Interest rate (Expressed in decimal form)

T  =  Time ( Expressed in years)

## Interest Word Problems - Examples

Example 1 :

Alex invested \$500 and received \$650 after three years. What had been the interest rate ?

Solution :

Step 1 :

Interest earned  =  A - P

Interest earned  =  650 - 500  =  150

And also,

P  =  500

T  =  3 years

Step 2 :

The interest formula is

I  =  PRT

Plug the values of I, P and T in the interest formula.

150  =  500 x R x 3

150  =  1500 x R

Divide both sides by 1500

150 / 1500  =  R

0.1  =  R

To convert decimal into percentage, multiply by 100.

(0.1 x 100) %  =  R

10 %  =  R

So, the interest rate is 10%.

Example 2 :

Arthur invests his inheritance of \$24000 in two different accounts which pays 6% and 5% annual interest. After one year, he received \$1340 in interest. How much did he invest in each account ?

Solution :

Step 1 :

Let "x" be the money invested at 6% rate.

Then, the money invested at 5% rate  =  24000 - x

Step 2 :

The interest formula is

I  =  PRT

Step 3 :

Interest earned at 6% rate is

I  =  (x)(0.06)(1)

I  =  0.06x

Step 4 :

Interest earned at 5% rate is

I  =  (24000 - x)(0.05)(1)

I  =  (24000 - x)(0.05)

I  =  1200 - 0.05x

Step 5 :

Adding the results of step 3 and step 4, we get

0.06x + 1200 - 0.05x  =  Total interest

0.01x + 1200  =  Total interest

In the question, the total interest is given \$1340.

Then, we have

0.01x + 1200  =  \$1340

Step 6 :

Solve for "x"

0.01x + 1200  =  \$1340

Subtract 1200 from both sides

0.01x  =  \$140

Divide both sides by 0.01

x  =  140 / 0.01

x  =  14000

Then,

24000 - x  =  24000 - 14000

24000 - x  =  10000

So, the money invested at 6% rate is \$14000 and 5% rate is \$10000.

Example 3 :

Part of \$5000 was invested at 5% and the other part at 6%. The 6% investment yielded \$135 more in profit than the other investment. How much money was invested at each rate ?

Solution :

Step 1 :

Let "x" be the money invested at 6% rate.

Then, the money invested at 6% rate  =  5000 - x

Step 2 :

The interest formula is

I  =  PRT

Step 3 :

Interest earned at 5% rate is

I  =  (x)(0.05)(1)

I  =  0.05x

Step 4 :

Interest earned at 6% rate is

I  =  (5000 - x)(0.06)(1)

I  =  (5000 - x)(0.06)

I  =  300 - 0.06x

Step 5 :

From, the given information, the difference between the interests earned at 6% and 5% is \$135.

(300 - 0.06x) - (0.05x)  =  135

300 - 0.06x - 0.05x  =  135

300 - 0.11x  =  135

300 - 135  =  0.11x

165  =  0.11x

Divide both sides by 0.11

165/0.11  =  x

1500  =  x

Then,

5000 - x  =  5000 - 1500

5000 - x  =  3500

So, the money invested at 5% rate is \$1500 and 6% rate is \$3500.

Example 4 :

Josh invested some money at 6% annual interest and three times as much at 8%. The total interest after one year was \$660. How much did he invest at each rate ?

Solution :

Step 1 :

Let "x" be the money invested at 6% rate.

Then, the money invested at 8% rate  =  3x

Step 2 :

The interest formula is

I  =  PRT

Step 3 :

Interest earned at 6% rate is

I  =  (x)(0.06)(1)

I  =  0.06x

Step 4 :

Interest earned at 8% rate is

I  =  (3x)(0.08)(1)

I  =  0.24x

Step 5 :

Adding the results of step 4 and step 5, we get

0.06x + 0.24x  =  Total interest

0.3x  =  Total interest

In the question, the total interest is given \$660.

Then, we have

0.3x  =  \$660

Step 6 :

Solve for "x"

0.3x  =  \$660

Divide both sides by 0.3.

x  =  660 / 0.3

x  =  2200

Then,

3x  =  3(2200)

3x  =  6600

So, the money invested at 6% rate is \$2200 and 8% rate is \$6600. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 