Question

you want to save in order to buy a car, in 6 years, without taking out a loan. you determine that youll need $38,000.00 for the purchase. if you deposit money into an ordinary annuity that yields 4.46% interest compounded monthly, how much will you need to deposit each month?
use this formula:
$pmnt = \frac{fv \times \frac{r}{n}}{(1+\frac{r}{n})^{nt}-1}$
enter the dollar amount rounded to the nearest cent.
your answer:
answer
view hint for question 8
question 9 (10 points)
you want to save in order to buy a car, in 4 years, without taking out a loan. you determine that youll need $18,000.00 for the purchase. if you deposit money into an ordinary annuity that yields 5.12% interest compounded monthly, how much will you need to deposit each month?
use this formula:
$pmnt = \frac{fv \times \frac{r}{n}}{(1+\frac{r}{n})^{nt}-1}$

Explanation:

For Question 8:

Step1: Define given values

$FV = 38000$, $r = 0.0446$, $n = 12$, $t = 6$

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

$\frac{0.0446}{12} \approx 0.003717$

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

$(1+0.003717)^{12 \times 6} = (1.003717)^{72} \approx 1.3004$

Step4: Compute denominator

$1.3004 - 1 = 0.3004$

Step5: Solve for $pmnt$

$pmnt = \frac{38000 \times 0.003717}{0.3004} \approx \frac{141.246}{0.3004} \approx 470.20$

For Question 9:

Step1: Define given values

$FV = 18000$, $r = 0.0512$, $n = 12$, $t = 4$

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

$\frac{0.0512}{12} \approx 0.004267$

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

$(1+0.004267)^{12 \times 4} = (1.004267)^{48} \approx 1.2253$

Step4: Compute denominator

$1.2253 - 1 = 0.2253$

Step5: Solve for $pmnt$

$pmnt = \frac{18000 \times 0.004267}{0.2253} \approx \frac{76.806}{0.2253} \approx 340.91$

Answer:

Question 8: $\$470.20$
Question 9: $\$340.91$