carla franz deposits $2,000 a year into her retirement account. if these funds have an average earning of 7…

carla franz deposits $2,000 a year into her retirement account. if these funds have an average earning of 7 percent over the 50 years until her retirement, what will be the value of her retirement account? note: do not round intermediate calculations. round your final answer to the nearest whole number. future value of retirement account

carla franz deposits $2,000 a year into her retirement account. if these funds have an average earning of 7 percent over the 50 years until her retirement, what will be the value of her retirement account? note: do not round intermediate calculations. round your final answer to the nearest whole number. future value of retirement account

Answer

Explanation:

Step1: Identify the formula for future - value of an ordinary annuity

The formula for the future - value of an ordinary annuity is $FVA = A\times\frac{(1 + r)^{n}-1}{r}$, where $A$ is the annual payment, $r$ is the interest rate per period, and $n$ is the number of periods.

Step2: Identify the values of $A$, $r$, and $n$

$A=$2000$, $r = 0.07$ (7% expressed as a decimal), and $n = 50$.

Step3: Substitute the values into the formula

$FVA=2000\times\frac{(1 + 0.07)^{50}-1}{0.07}$. First, calculate $(1 + 0.07)^{50}$. Using the formula $a^{b}$, where $a = 1.07$ and $b = 50$, we have $(1.07)^{50}\approx29.457027$. Then, $(1.07)^{50}-1\approx29.457027 - 1=28.457027$. $\frac{(1.07)^{50}-1}{0.07}=\frac{28.457027}{0.07}\approx406.52896$. Finally, $FVA = 2000\times406.52896=$813057.92$.

Step4: Round the final answer

Rounding to the nearest whole number, $FVA=$813058$.

Answer:

$813058$