Math money problem

Question

Sally invests $4000 in a savings account which compounds interest monthly. After 10 years, she has a balance of $4,614.53. What is the annual interest rate of the account, rounded to the nearest 0.01%?

Answer 1

A = P(1 + r/n)^nt

 

4614.53 = 4000(1 + r/12)¹²⁽¹⁰⁾   divide both sides by 4000

1.1536325 = (1 + r/12)¹²⁰    raise both sides to the 1/120 power

 

1.1536325^1/120 = (1 + r/12)^120(1/120)

1.001191673 = 1 + r/12       subtract one from both sides

.001191673 = r/12                multiply both sides by 12

.014300076 = r

.01 ∼ r