question 9 (10 points)\nyou want to save in order to buy a car, in 5 years, without taking out a loan. you…

question 9 (10 points)\nyou want to save in order to buy a car, in 5 years, without taking out a loan. you determine that youll need $26,000.00 for the purchase. if you deposit money into an ordinary annuity that yields 5.23% interest compounded monthly, how much will you need to deposit each month?\nuse this formula:\n$pmt=\frac{fv\times\frac{r}{n}}{(1 + \frac{r}{n})^{nt}-1}$\nenter the dollar amount rounded to the nearest cent.\nyour answer:\nanswer

question 9 (10 points)\nyou want to save in order to buy a car, in 5 years, without taking out a loan. you determine that youll need $26,000.00 for the purchase. if you deposit money into an ordinary annuity that yields 5.23% interest compounded monthly, how much will you need to deposit each month?\nuse this formula:\n$pmt=\frac{fv\times\frac{r}{n}}{(1 + \frac{r}{n})^{nt}-1}$\nenter the dollar amount rounded to the nearest cent.\nyour answer:\nanswer

Answer

Explanation:

Step1: Identify the values

$FV = 26000$, $r=0.0523$ (5.23% as a decimal), $n = 12$ (compounded monthly), $t = 5$ years.

Step2: Calculate the monthly interest rate and number of periods

The monthly interest rate $i=\frac{r}{n}=\frac{0.0523}{12}$. The number of periods $mt=12\times5 = 60$.

Step3: Substitute values into the formula

$pmt=\frac{FV\times i}{(1 + i)^{mt}-1}=\frac{26000\times\frac{0.0523}{12}}{(1+\frac{0.0523}{12})^{60}-1}$. First, calculate $(1+\frac{0.0523}{12})^{60}$. Let $x=\frac{0.0523}{12}\approx0.00435833$. Then $(1 + x)^{60}\approx1.29397$. Next, $26000\times\frac{0.0523}{12}\approx113.9167$. And $(1+\frac{0.0523}{12})^{60}-1\approx1.29397 - 1=0.29397$. Finally, $pmt=\frac{113.9167}{0.29397}\approx387.49$.

Answer:

$387.49$