you want to save in order to buy a car, in 6 years, without taking out a loan. you determine that youll need…

you want to save in order to buy a car, in 6 years, without taking out a loan. you determine that youll need $31,000.00 for the purchase. if you deposit money into an ordinary annuity that yields 5.33% 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

you want to save in order to buy a car, in 6 years, without taking out a loan. you determine that youll need $31,000.00 for the purchase. if you deposit money into an ordinary annuity that yields 5.33% 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

$FV = 31000$, $r=0.0533$, $n = 12$, $t = 6$

Step2: Calculate the exponent part

$(1+\frac{r}{n})^{nt}=(1+\frac{0.0533}{12})^{12\times6}$ $=(1 + 0.00444167)^{72}$ $\approx1.37977$

Step3: Calculate the numerator

$FV\times\frac{r}{n}=31000\times\frac{0.0533}{12}$ $=31000\times0.00444167$ $\approx137.6917$

Step4: Calculate the denominator

$(1+\frac{r}{n})^{nt}-1=1.37977 - 1=0.37977$

Step5: Calculate the monthly payment

$pmt=\frac{FV\times\frac{r}{n}}{(1+\frac{r}{n})^{nt}-1}=\frac{137.6917}{0.37977}\approx362.57$

Answer:

$362.57$