Problema Solution
Suppose you have
$13,000
to invest. Which of the two rates would yield the larger amount in
1 year​:
8%
compounded
monthly
or
7.89%
compounded​ continuously?
Answer provided by our tutors
P = $13,000
t = 1 year
A = the future value
Compounded monthly at rate of r = 0.08 or 8%:
A = P(1 + r/12)^t
A = 13000(1 + 0.08/12)
A = $13,086.67
Compounded​ continuously at rate of r = 0.08 or 8%:
A=Pe^(rt)
A=13000e^(0.08*1)
A = $14,082.73
Since 14,082.73 > 13,086.67 the continuous compounding will yield the largest amount.