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

Explanation:

Answer 2

3.73%

Explanation:

The formula is

`A=P(1+(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+(r)/(4))^(40)`

`(5809.81)/(4000)=(1+(r)/(4))^(40)`

`((5809.81)/(4000))^{(1)/(40)}=1+(r)/(4)`

`(1.45)^{(1)/(40)}=1+(r)/(4)`

`1.0093 = 1+(r)/(4)`

Subtracting 1 on both sides

`0.0093=(r)/(4)`

`r=0.0093*4`

r=0.03732

Rate is 3.73%