Question

you build an annuity by investing ( p ) dollars every month at interest rate ( r ), compounded monthly. find the amount ( a ) accrued after ( n ) months using the formula a = pleft \frac{(1 + r/12)^n - 1}{r/12}
ight where ( r ) is in decimal form. (round your answer to two decimal places.) ( p = $116, r = 0.09, n = 52 ) months ( a = $ ) enter a number resources read it watch it submit answer

Explanation:

Step1: Identify given values

$P=116$, $r=0.09$, $n=52$

Step2: Calculate monthly rate

$\frac{r}{12} = \frac{0.09}{12} = 0.0075$

Step3: Calculate $(1+\frac{r}{12})^n$

$(1+0.0075)^{52} \approx 1.47087$

Step4: Subtract 1 from the result

$1.47087 - 1 = 0.47087$

Step5: Divide by monthly rate

$\frac{0.47087}{0.0075} \approx 62.7827$

Step6: Multiply by $P$

$A = 116 \times 62.7827 \approx 7282.79$

Answer:

$\$7282.79$