Problema Solution
find the accumulated value of an investment of $10,000 for 4 years at an interest rate of 5% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.
Answer provided by our tutors
Let
P = $10,000
t = 4 years
r = 0.05 or 5% annual interest rate
A = future value (accumulated value)
a. what is the accumulated value if the money is compounded semiannually?
n = 2
A=P(1+ r/n)^(nt)
A = 10000(1 + 0.05/2)^(2*4)
........
click here to see the calculation for A
........
A = $12,184.03
b. What is the accumulated value if the money is compounded quarterly?
n = 4
A=P(1+ r/n)^(nt)
A = 10000(1 + 0.05/4)^(4*4)
........
click here to see the calculation for A
........
A = $12,198.90
c. What is the accumulated value if the money is compounded monthly?
n = 12
A=P(1+ r/n)^(nt)
A = 10000(1 + 0.05/12)^(12*4)
........
click here to see the calculation for A
........
A = $12,208.96
d. What is the accumulated value if the money is compounded continuously?
A=Pe^rt
A = 10000*e^(0.05*4)
........
click here to see the calculation for A
........
A = $12,214.03