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Math

QuestionFind the ending amount with compound interest for \$700 at 3\% compounded annually.

Studdy Solution

STEP 1

Assumptions1. The principal amount is $700. The interest rate is3%
3. The interest is compounded annually

STEP 2

The formula for compound interest is given byA=(1+rn)ntA = \left(1 + \frac{r}{n}\right)^{nt}where- AA is the amount of money accumulated after n years, including interest. - $$ is the principal amount (the initial amount of money). - $r$ is the annual interest rate (in decimal). - $n$ is the number of times that interest is compounded per year. - $t$ is the time the money is invested for in years.

STEP 3

Since the interest is compounded annually, nn is1. Also, as we are looking for the formula for the ending amount including compound interest, we don't have a specific value for tt. So, the formula becomesA=(1+r)tA = \left(1 + r\right)^{t}

STEP 4

Now, plug in the given values for the principal amount and interest rate to write the formula.
A=$700(1+3%)tA = \$700 \left(1 +3\%\right)^{t}

STEP 5

Convert the percentage to a decimal value.
3%=0.033\% =0.03A=$700(1+0.03)tA = \$700 \left(1 +0.03\right)^{t}

STEP 6

implify the formula.
A=$700×(1.03)tA = \$700 \times (1.03)^{t}So, the formula for finding the ending amount including compound interest is A=$700×(1.03)tA = \$700 \times (1.03)^{t}.

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