7. 0/7.14 points follow the link future value of annuity formula. this will direct you to a spreadsheet…
7. 0/7.14 points follow the link future value of annuity formula. this will direct you to a spreadsheet download that may be useful for checking your work for the exercise. margo starts an individual retirement account (ira) by depositing $350 at the beginning of each month into an account that earns 5.5% interest compounded monthly. if margo continues this plan for 20 years, what will be the value (in dollars) of her account? (round your answer to the nearest cent. see example 1 in this section.)
Answer
Answer:
We use the future - value of an annuity - due formula (FV = A\times\frac{(1 + \frac{r}{n})^{nt}-1}{\frac{r}{n}}\times(1+\frac{r}{n})), where (A = 350), (r=0.055), (n = 12), and (t = 20).
First, calculate the exponent ((nt)=(12\times20)=240) and (\frac{r}{n}=\frac{0.055}{12}).
(1+\frac{r}{n}=1+\frac{0.055}{12}\approx1.0045833)
((1 + \frac{r}{n})^{nt}=(1.0045833)^{240}\approx3.00447)
((1 + \frac{r}{n})^{nt}-1\approx3.00447 - 1=2.00447)
(\frac{(1 + \frac{r}{n})^{nt}-1}{\frac{r}{n}}=\frac{2.00447}{\frac{0.055}{12}}\approx\frac{2.00447}{0.0045833}\approx437.34)
(FV = 350\times437.34\times1.0045833\approx350\times439.33\approx153765.50)
So the value of her account is ($153765.50)