you want to save in order to buy a car, in 5 years, without taking out a loan. you determine that you’ll…

you want to save in order to buy a car, in 5 years, without taking out a loan. you determine that you’ll 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? use this formula: $pmt=\frac{fv\times\frac{r}{n}}{(1 + \frac{r}{n})^{nt}-1}$ enter the dollar amount rounded to the nearest cent. your answer: answer
Answer
Explanation:
Step1: Identify the values
$FV = 26000$, $r=0.0523$, $n = 12$, $t = 5$.
Step2: Calculate the monthly interest rate
$i=\frac{r}{n}=\frac{0.0523}{12}$.
Step3: Calculate the number of periods
$mt=12\times5 = 60$.
Step4: Substitute values into the formula
$pmt=\frac{26000\times\frac{0.0523}{12}}{(1 + \frac{0.0523}{12})^{60}-1}$. First, calculate the denominator: $(1+\frac{0.0523}{12})^{60}\approx1.29177$. Then $(1+\frac{0.0523}{12})^{60}-1\approx0.29177$. The numerator is $26000\times\frac{0.0523}{12}\approx113.783$. $pmt=\frac{113.783}{0.29177}\approx390.00$.
Answer:
$390.00$