question 15 (4.5 points) you want to save in order to buy a car, in 4 years, without taking out a loan. you…

question 15 (4.5 points) you want to save in order to buy a car, in 4 years, without taking out a loan. you determine that youll need $33,000.00 for the purchase. if you deposit money into an ordinary annuity that yields 5.15% 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 previous page next page page 3 of 5

question 15 (4.5 points) you want to save in order to buy a car, in 4 years, without taking out a loan. you determine that youll need $33,000.00 for the purchase. if you deposit money into an ordinary annuity that yields 5.15% 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 previous page next page page 3 of 5

Answer

Explanation:

Step1: Identify the formula variables

The formula for the future - value of an ordinary annuity is $FVA = pmt\times\frac{(1 + \frac{r}{n})^{nt}-1}{\frac{r}{n}}$, where $FVA$ is the future value of the annuity, $pmt$ is the payment per period, $r$ is the annual interest rate (in decimal), $n$ is the number of compounding periods per year, and $t$ is the number of years. We know that $FVA=$33000$, $r = 0.0515$ (since $5.15%=0.0515$), $n = 12$ (compounded monthly), and $t = 4$. We need to solve for $pmt$.

Step2: Rearrange the formula for $pmt$

From $FVA = pmt\times\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}}$, we can get $pmt=\frac{FVA\times\frac{r}{n}}{(1 + \frac{r}{n})^{nt}-1}$.

Step3: Substitute the values

Substitute $FVA = 33000$, $r=0.0515$, $n = 12$, and $t = 4$ into the formula. First, calculate $(1+\frac{r}{n})^{nt}=(1+\frac{0.0515}{12})^{12\times4}=(1+\frac{0.0515}{12})^{48}$. $1+\frac{0.0515}{12}=1 + 0.00429167\approx1.00429167$. $(1.00429167)^{48}\approx1.23197$. Then, $\frac{r}{n}=\frac{0.0515}{12}\approx0.00429167$. $pmt=\frac{33000\times0.00429167}{1.23197 - 1}$. $33000\times0.00429167 = 141.62511$. $1.23197-1=0.23197$. $pmt=\frac{141.62511}{0.23197}\approx610.44$.

Answer:

$610.44$