Answer:
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
