question 8 (10 points)\nyou want to save in order to buy a car, in 3 years, without taking out a loan. you…

question 8 (10 points)\nyou want to save in order to buy a car, in 3 years, without taking out a loan. you determine that youll need $28,000.00 for the purchase. if you deposit money into an ordinary annuity that yields 4.55% interest compounded monthly, how much will you need to deposit each month?\nuse this formula:\n$pmt=\frac{fv\times\frac{r}{n}}{(1 + \frac{r}{n})^{nt}-1}$\nenter the dollar amount rounded to the nearest cent.\nyour answer:

question 8 (10 points)\nyou want to save in order to buy a car, in 3 years, without taking out a loan. you determine that youll need $28,000.00 for the purchase. if you deposit money into an ordinary annuity that yields 4.55% interest compounded monthly, how much will you need to deposit each month?\nuse this formula:\n$pmt=\frac{fv\times\frac{r}{n}}{(1 + \frac{r}{n})^{nt}-1}$\nenter the dollar amount rounded to the nearest cent.\nyour answer:

Answer

Explanation:

Step1: Identify the values

$FV = 28000$ (future - value, the amount needed for the car), $r=0.0455$ (annual interest rate), $n = 12$ (compounding periods per year), $t = 3$ (number of years).

Step2: Calculate the number of periods and interest rate per period

The number of periods $mt=12\times3 = 36$. The interest rate per period $\frac{r}{n}=\frac{0.0455}{12}$.

Step3: Substitute values into the formula

$pmt=\frac{FV\times\frac{r}{n}}{(1 + \frac{r}{n})^{mt}-1}=\frac{28000\times\frac{0.0455}{12}}{(1+\frac{0.0455}{12})^{36}-1}$. First, calculate $(1+\frac{0.0455}{12})^{36}$. Let $x=\frac{0.0455}{12}\approx0.003792$. Then $(1 + x)^{36}\approx1.14477$. Next, $28000\times\frac{0.0455}{12}\approx106.17$. $(1+\frac{0.0455}{12})^{36}-1\approx0.14477$. $pmt=\frac{106.17}{0.14477}\approx733.35$.

Answer:

$733.35$