Interest Word Problems

Sam invested 11000 in an acct that pays 11% apr. How much additional money must be invested in an acct that pays an apr of 14% so that the total interest is equal to the interest on the two investments at the rate of 12%?

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Nov 05, 2010
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by: Karin

This is a great problem!

Let's write the numerical equation step by step from the problem.

Let x = the amount of additional money needed.

Sam invested 11000 in an acct that pays 11% apr. (11000 * .11)

How much additional money must be invested in an acct that pays an apr of 14%
+.14x

so that the total interest is equal

=

to the interest on the two investments at the rate of 12%

.12(11000 +x)

Now let's put it all together.

11000(.11) + .14x = .12(11000 +x)

Step 1: Compute 11000*.11 and use the distributive property.

1210 + .14x = 1320 +.12x

Step 2: Get the variables on the left hand side by subtracting .12x from both sides.

1210 + 14x - .12x = 1320 + 12.x - .12x

1210 +.02x = 1320

Step 3: Get the constants on the right hand side by subtracting 1210 from both sides.

1210 - 1210 + .02x = 1320 - 1210

.02x = 110

Step 4: Divide both sides by .02

.02x/.02 = 110/.02

x = 5500

The addition amount should be 5500.

Let's check:

11000(.11) + .14(5500) = .12(11000+5500)
1980 = 1980

The interest is equal for both investments.

Hope this helps.

Karin

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