Problema Solution
If 7000 dollars is invested at an interest rate of 10 percent per year, find the value of the investment at the end of 5 years for the following compounding methods.
(a) Annual:
(b) Semiannual:
(c) Monthly:
(d) Daily:
(e) Continuously:
Answer provided by our tutors
P = $7,000 is the principal
r = 0.10 the annual interest rate of 10%
t = 5 years
(a) Annual:
A = P(1 + i)^n
m = 1 is the number of compounding periods per year
n = m*t = 1*5 = 5 is the number of compounding periods
i = r/m = 0.10 is the interest rate per period
A = 7000(1 + 0.10)^5
A = $11,273.57
(b) Semiannual:
A = P(1 + i)^n
m = 2 is the number of compounding periods per year
n = m*t = 2*5 = 10 is the number of compounding periods
i = r/m = 0.10/2 = 0.05 is the interest rate per period
A = 7000(1 + 0.05)^10
A = $11,402.26
(c) Monthly:
A = P(1 + i)^n
m = 12 is the number of compounding periods per year
n = m*t = 12*5 = 60 is the number of compounding periods
i = r/m = 0.10/12 = 0.1/12 is the interest rate per period
A = 7000(1 + 0.1/12)^60
A = $11,517.16
(d) Daily:
A = P(1 + i)^n
m = 365 is the number of compounding periods per year
n = m*t = 365*5 = 1825 is the number of compounding periods
i = r/m = 0.10/365 = 0.1/365 is the interest rate per period
A = 7000(1 + 0.1/365)^1825
A = $11,540.26
(e) Continuously:
A = P*e^(r*t), where e = 2.71828 is Napier's constant
A = 7000*e^(0.1*5)
A = $11,541.05