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:\nanswer

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:\nanswer

Answer

Explanation:

Step1: Identify the values

$FV = 28000$, $r=0.0455$, $n = 12$ (monthly compounding), $t = 3$.

Step2: Calculate the exponent and the denominator part

First, calculate $(1+\frac{r}{n})^{nt}=(1 +\frac{0.0455}{12})^{12\times3}$. Let $x=\frac{0.0455}{12}\approx0.003792$, then $(1 + x)^{36}\approx1.14777$. The denominator $(1+\frac{r}{n})^{nt}-1\approx1.14777 - 1=0.14777$.

Step3: Calculate the numerator part

The numerator is $FV\times\frac{r}{n}=28000\times\frac{0.0455}{12}\approx28000\times0.003792 = 106.176$.

Step4: Calculate the payment amount

$pmt=\frac{FV\times\frac{r}{n}}{(1+\frac{r}{n})^{nt}-1}=\frac{106.176}{0.14777}\approx718.53$.

Answer:

$718.53$