Problema Solution
If 45100 dollars is invested at an interest rate of 9 percent per year, find the value of the investment at the end of 5 years for the following compounding methods.
Annual
Semiannual
Monthly
Daily
Continuously
Answer provided by our tutors
P = $45,100 the principal
r = 0.09 or 9% annual interest rate
t = 5 years
n = the number of compounding periods
A = the future value
Annual compounding:
n = 1*t = 1*5 = 5 compounding periods
A = P(1 + r)^n
A = 45100(1 + 0.09)^5
A = $69,391.94
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Semiannual compounding:
n = 2*t = 2*5 = 10 compounding periods
A = P(1 + r/2)^n
A = 45100(1 + 0.09/2)^10
A = $70,038.92
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Monthly compounding:
n = 12*t = 12*5 = 60 compounding periods
A = P(1 + r/12)^n
A = 45100(1 + 0.09/12)^60
A = $70,612.21
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Daily compounding:
n = 365*t = 365*5 = 1,825 compounding periods
A = P(1 + r/365)^n
A = 45100(1 + 0.09/365)^1825
A = $70,726.96
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Continuously compounding
A = P(e^(rt))
e = 2.7183
A = 45100(2.7183^(0.09*5))
A = $70,731.09
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