you deposited 500 in an account that pays 3.25 annual interest compounded monthly. About how long does it take for the balance to quadruple?

42 years, 9 months

Step-by-step explanation:

Using the compound interest formula Accrued Amount = P (1 + r/n) ^ (nt)

where Accrued amount (A) which is quadruple the initial deposit

A = 4 x 500 = $2000

P = principal; $500

r = 3.25% = 0.0325

t = number of years

n = number of times interest is compounded = 12 for monthly

Therefore

2000 = 500 (1 + 0.0325/12) ^ (12t)

Therefore

(1.002708) ^12t = 2000/500

(1.002708) ^12t = 4

finding the log of both sides

12t x log 1.002708 = log 4

12t x 0.001174 = 0.6021

12t = 0.6021/0.001174

12t = 512.83

t = 512.83/12

t = 42.7

which is estimated as 42 years, (0.7 x 12 = 9) months

hence it takes about 43 years to quadruple the deposit