IXL - Continuously compounded interest: word problems (Algebra 2 practice)

Gavin and Deb deposit $1,000.00 into a savings account which earns 13% interest compounded continuously. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend?

Use the formula

where

is the balance (final amount),

is the principal (starting amount), e is the base of natural logarithms (≈2.71828),

is the interest rate expressed as a decimal, and

is the time in years.

Round your answer to the nearest cent.

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Learn with an example

question

Perry puts $800.00 into an account to use for school expenses. The account earns 5% interest, compounded continuously. How much will be in the account after 9 years?

Use the formula

where

is the balance (final amount),

is the principal (starting amount), e is the base of natural logarithms (≈2.71828),

is the interest rate expressed as a decimal, and

is the time in years.

Round your answer to the nearest cent.

key idea

Continuously compounded interest:

The variables in the equation are

and

The letter e is a constant.

is the balance (final amount).

is the principal (starting amount).

e is the base of natural logarithms.

is the interest rate expressed as a decimal.

is the time in years.

solution

You want to find the balance,

First, list the other variables in the equation

and specify their given values.

$800.00

0.05

9 years

Now plug these values into the equation and solve for

Plug in

800

0.05

and

800

0.05

Plug in

800

0.05

and

800

0.45

≈

1,254.64974839

≈

Round to the nearest cent

$1,254.65

Round to the nearest cent

To the nearest

cent,

$1,254.65 will be in the account.

Looking for more? Try these:

Lesson: Exponential growth

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Not feeling ready yet? These can help:

CC.4Compound interest: word problems

CC.3Solve exponential equations using natural logarithms

Lesson: Exponential growth

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