question 8 (10 points)\nyou want to save in order to buy a car, in 4 years, without taking out a loan. you…

question 8 (10 points)\nyou want to save in order to buy a car, in 4 years, without taking out a loan. you determine that youll need $28,500.00 for the purchase. if you deposit money into an ordinary annuity that yields 5.49% interest compounded monthly, how much will you need to deposit each month?\nuse this formula:\n$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 4 years, without taking out a loan. you determine that youll need $28,500.00 for the purchase. if you deposit money into an ordinary annuity that yields 5.49% interest compounded monthly, how much will you need to deposit each month?\nuse this formula:\n$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: Define variables

$FV = 28500$, $r = 0.0549$, $n = 12$, $t = 4$

Step2: Calculate $\frac{r}{n}$

$\frac{0.0549}{12}=0.004575$

Step3: Calculate $(1+\frac{r}{n})^{nt}$

$(1+0.004575)^{12\times4}=(1.004575)^{48}\approx1.2447$

Step4: Calculate denominator

$1.2447 - 1 = 0.2447$

Step5: Compute numerator

$28500\times0.004575=130.3875$

Step6: Solve for $pmt$

$pmt=\frac{130.3875}{0.2447}\approx532.84$

Answer:

$$532.84$