Problema Solution
An initial deposit of $42,000 grows at an annual rate of 6% for 25 years. Compare the final balances resulting from continuous compounding and annual compounding. (Round your answers to the nearest cent.)
from continuous compounding
from annual compounding
Answer provided by our tutors
P = $42,000
r = 6% = 0.06
t = 25 years
annual compounding
A = P(1 + i)^n
m = 1 the number of compounding period per year
n = 25 the number of compounding periods
i = r/m = 6% = 0.06
A = 42000(1 + 0.06)^25
A = $180,258.57
continuous compounding
A = P*e^(r*t)
A = 42000*e^(0.06*25)
e = 2.71828182846
A = $188,230.94
the final balance from continuous compounding is bigger then the final balance from annual compounding.