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

question 10 (10 points)\nyou want to save in order to buy a car, in 5 years, without taking out a loan. you determine that you’ll need $34,000.00 for the purchase. if you deposit money into an ordinary annuity that yields 5.38% interest compounded monthly, how much will you need to deposit each month?\nuse this formula:\n$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 10 (10 points)\nyou want to save in order to buy a car, in 5 years, without taking out a loan. you determine that you’ll need $34,000.00 for the purchase. if you deposit money into an ordinary annuity that yields 5.38% interest compounded monthly, how much will you need to deposit each month?\nuse this formula:\n$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

$FV = 34000$, $r=0.0538$ (5.38% as a decimal), $n = 12$ (compounded monthly), $t = 5$ years.

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

$i=\frac{r}{n}=\frac{0.0538}{12}$, $nt=12\times5 = 60$.

Step3: Substitute values into the formula

$pmt=\frac{34000\times\frac{0.0538}{12}}{(1 + \frac{0.0538}{12})^{60}-1}$. First, calculate $(1+\frac{0.0538}{12})^{60}$. Let $x=\frac{0.0538}{12}\approx0.0044833$. Then $(1 + x)^{60}\approx1.29177$. The numerator is $34000\times\frac{0.0538}{12}\approx34000\times0.0044833 = 152.4322$. The denominator is $1.29177-1 = 0.29177$. $pmt=\frac{152.4322}{0.29177}\approx522.43$.

Answer:

$522.43$