find the savings plan balance after 3 years with an apr of 9% and monthly payments of $300. the balance is $…

find the savings plan balance after 3 years with an apr of 9% and monthly payments of $300. the balance is $ . (do not round until the final answer. then round to the nearest cent as needed.)

find the savings plan balance after 3 years with an apr of 9% and monthly payments of $300. the balance is $ . (do not round until the final answer. then round to the nearest cent as needed.)

Answer

Explanation:

Step1: Identify the formula

The formula for the future - value of a regular savings plan (ordinary annuity) is $F = P\times\frac{(1 + r)^{n}-1}{r}$, where $P$ is the payment per period, $r$ is the interest rate per period, and $n$ is the number of periods. The annual percentage rate (APR) is 9% or 0.09. Since the payments are monthly, the interest rate per month $r=\frac{0.09}{12}=0.0075$. The number of years is 3, and since there are 12 months in a year, the number of periods $n = 3\times12=36$. The monthly payment $P = 300$.

Step2: Substitute the values into the formula

$F=300\times\frac{(1 + 0.0075)^{36}-1}{0.0075}$. First, calculate $(1 + 0.0075)^{36}$. Using the formula $a^{b}$, where $a = 1.0075$ and $b = 36$, we have $(1.0075)^{36}\approx1.292277$. Then, $(1.0075)^{36}-1\approx1.292277 - 1=0.292277$. $\frac{(1.0075)^{36}-1}{0.0075}=\frac{0.292277}{0.0075}\approx38.97027$. Finally, $F = 300\times38.97027=11691.081$.

Answer:

$11691.08$