Answer:
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 = 63000
r = 2.55% = 2.55/100 = 0.0255
n = 12 because it was compounded 12 times in a year.
Therefore, function, C(t), that represents the amount of money in the account t years after the account is opened is
C(t) = 63000(1 + 0.0255/12)^12t
C(t) = 63000(1.002125)^12t
For C(t) = 100000,
100000 = 63000(1.002125)^12t
100000/63000 = (1.002125)^12t
1.587 = 1.002125)^12t
Taking log of both sides
Log 1.587 = log 1.002125)^12t
Log 1.587 = 12tlog 1.002125)^
0.2005 = 12t × 0.00092
0.2005 = t × 0.01104
t = 0.2005/0.01104
t = 18.16 years
