Answer:it will take over 10 years
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 2000
r = 4% = 4/100 = 0.04
n = 12 because it was compounded monthly(12 times in a year)
A= 3000
Therefore,
3000 = 2000(1+0.04/12)^12 × t
3000/2000= (1.0033)^12t
1.5 = (1.0033)^12t
Taking log of both sides
Log 1.5 = log(1.0033)^12t
Log 1.5 = 12tlog(1.0033)
0.176 = 12t × 0.00143 = 0.01716t
t = 0.176/0.01716 = 10.26
