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# the mAth

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Ken's parents invest \$1,000 in the year 2013 for his college fund. The account is compounded annually.

In 18 years they would like to make another \$800 in interest.

What interest rate would be required for this to happen?

Apr 16, 2015

#1
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Interest compounded annually is modeled by the exponential function, A=A0(1+r)t where r is the growth rate, A0 is the initial amount invested, A is the final amount and t is the number of years.

In this problem:

A0=1000t=18A=1800

The equation that models the bank account is:

1800=1000(1+r)18

To solve for r, first divide both sides by 10000.

18001000=(1000(1+r)18)1000

1.8=(1+r)18

You must now take the 18th root of each side.

1.03319=1+r

0.03319=r

After converting the decimal to a percent,the rate is approximately 3.32%.

Apr 16, 2015

#1
+5

Interest compounded annually is modeled by the exponential function, A=A0(1+r)t where r is the growth rate, A0 is the initial amount invested, A is the final amount and t is the number of years.

In this problem:

A0=1000t=18A=1800

The equation that models the bank account is:

1800=1000(1+r)18

To solve for r, first divide both sides by 10000.

18001000=(1000(1+r)18)1000

1.8=(1+r)18

You must now take the 18th root of each side.

1.03319=1+r

0.03319=r

After converting the decimal to a percent,the rate is approximately 3.32%.

shaniab29544 Apr 16, 2015