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DETAILS
Complete the table for a savings account in which interest is compounded continuously. (Round any dollar amount
Amount After
10 Years
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Initial
Investment
$4000
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PREVIOUS ANSWERS
DETAILS
Annual
% Rate
2%
Time to
Double
LARPRECALCRMRP7 3.5.014.
PREVIOUS ANSWERS
Xyr $4885.61
LARPRECALCRMRP7 3.5.016.
Complete the table for a savings account in which interest is compounded continuously. (Round any dollar amount to

Answer 1

• doubling time: 34.6574 years
• after 10 years: $4885.61

Explanation:

You want the doubling time for an investment earning 2% interest compounded continuously, and the value of a $4000 investment after 10 years at that rate.

Compound interest

The formula for continuously compounded interest is ...

A = Pe^(rt)

Doubling time

When A = 2P, and r = 0.02, the value of t is ...

2 = e^(0.02t)

ln(2) = 0.02t . . . . take natural logs

t = ln(2)/0.02 ≈ 34.6574

The time to double the investment is 34.6574 years.

10 years

The value after 10 years is ...

A = 4000·e^(0.02·10) ≈ 4885.61

The amount after 10 years is $4885.61.

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