Problema Solution
An initial deposit of $34,000 grows at an annual rate of 9% for 22 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= $34,000
r = 9% = 0.09
t = 22 years
e = 2.718281828
from continuous compounding
A = P(e^(r*t))
A = 34000(e^(0.09*22))
A = 34000 (e^1.98)
A = $246,253.26
from annual compounding
A = P(1 + i)^n
n = 22 is the number of compounding periods
m = 1 is the number of compounding periods per year
i = r/m = r = 0.09
A = 34000(1 + 0.09)^22
A = $226,392.41
the final balances from continuous compounding is bigger then the the final balances from annual compounding that is
$246,253.26 > $226,392.41