QuestionBode invests \$250 at 3% simple interest. Find the formula and balance at year 14. Options: A, B, C, D.

Studdy Solution

STEP 1

Assumptions1. The initial investment amount is $250. The annual simple interest rate is3%
3. Bode makes no deposits or withdrawals from the account4. The interest is calculated annually, not compounded5. We need to find the balance at the beginning of year14

STEP 2

The formula for simple interest is given by $A(n) = + n \cdot r \cdot$ where- $A(n)$ is the account balance at the beginning of year $n$ - $$ is the principal amount (the initial investment) - $r$ is the annual interest rate- $n$ is the number of years

STEP 3

Plug in the given values for the principal amount and the interest rate into the formula.
$A(n) = \$250 + n \cdot3\% \cdot \$250$

STEP 4

Convert the percentage to a decimal value.
$3\% =0.03$ $A(n) = \$250 + n \cdot0.03 \cdot \$250$

STEP 5

This formula can be simplified to $A(n) = \$250 + n \cdot0.03 \cdot \$250 = \$250 +0.03n \cdot \$250$

STEP 6

Now, we can use this formula to find the account balance at the beginning of year14. Plug in $n =14$ into the formula.
$A(14) = \$250 +0.03 \cdot14 \cdot \$250$

STEP 7

Calculate the account balance at the beginning of year14.
$A(14) = \$250 +0.03 \cdot14 \cdot \$250 = \$355$ So, the correct answer is A. $A(n)=250+(n)(0.03 \cdot250) ; \$355.00$

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