Question

Suppose you have $2,000 to invest. In 4 years, you would like to purchase a new car and want a down payment of $3,500. What interest rate would you need to have if the interest is compounded monthly?

Answer 1

Answer:

Rate = 14.07%

Step-by-step explanation:

$A= P(1+\frac{r}{n})^{nt}$

A= 3500

P= 2000

n = 12

t = 4

$3500= 2000(1+\frac{r}{12})^{4 \times 12}\\\\\frac{3500}{2000} = (1+\frac{r}{12})^{48}\\\\\frac{7}{4} = (1+\frac{r}{12})^{48}\\\\1.75 = (1+\frac{r}{12})^{48}\\\\\sqrt[48]{1.75} = (1+\frac{r}{12})\\\\\sqrt[48]{1.75}-1 = \frac{r}{12}\\\\0.01172688 = \frac{r}{12}\\\\r = 0.01172688 \times 12 = 0.14072267\\\\r \% = 14.07%$