Question

Aaron invested $4000 in an account that paid an interest rate r compounded quarterly. After 10 years he has $5809.81. The compound interest formula is A=P (1 +r/n)^nt, where P is the principal (the initial investment), A is the total amount of money (principal plus interest), r is the annual interest rate, t is the time in years, and n is the number of compounding periods per year.
a. Divide both sides of the formula by P and then use logarithms to rewrite the formula without an exponent. Show your work.

b. Using your answer for part a as a starting point, solve the compound interest formula for the interest rate, r.

c. Use your equation from part a to determine the interest rate.

Answer 1

Answer:A

Step-by-step explanation:

Answer 2

Answer:

3.73%

Step-by-step explanation:

The formula is

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

Here we are given that A= 5809.81 , P=4000 , t=10 years and n = 4 (compounded quaterly)

Now we have to substitute them in the formula

$5809.81=4000(1+\frac{r}{4})^{40}$

$\frac{5809.81}{4000}=(1+\frac{r}{4})^{40}$

$(\frac{5809.81}{4000})^{\frac{1}{40}}=1+\frac{r}{4}$

$(1.45)^{\frac{1}{40}}=1+\frac{r}{4}$

$1.0093 = 1+\frac{r}{4}$

Subtracting 1 on both sides

$0.0093=\frac{r}{4}$

$r=0.0093*4$

r=0.03732

Rate is 3.73%