# algebra 2

The amount of money in an account with continuously compounded interest is given by the formula A=Pe^rt , where P is the principal, r is the annual interest rate, and t is the time in years. Calculate to the nearest hundredth of a year how long it takes for an amount of money to double if interest is compounded continuously at 6.2%. Round to the nearest tenth.

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1. This means that
A/P=2, or
e^(rt)=2
log(e^(rt))=loge2
rt=loge2
t=(loge2)/r
=(loge2)/0.062 years
=?

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2. 👎
2. This means that
A/P=2, or
e^(rt)=2
log(e^(rt))=loge2
rt=loge2
t=(loge2)/r
=(loge2)/0.062 years
=?

Note:
This is actually the rule of 69.31, as follows:
The number of years to double money multiplied by the interest rate of p% compounded continuously is 69.31.

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3. Eli deposited \$1400 at 6.5% interest compounded quarterly. How much money will he have at the end of 8 years?

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4. An initial amount of money is placed in an account at an interest rate of per year, compounded continuously. After three years, there is in the account. Find the initial amount placed in the account. Round your answer to the nearest cent.

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5. 0.3=10^06x

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