Problema Solution
Suppose that you have $4000 to invest. Which investment yields the greater return over 10 years: 7.5% compounded continuously or 7.6% compounded semiannually
Answer provided by our tutors
P = $4,000 the principal
r = 0.075 or 7.5% annual interest rate
m = 2 compounding period per year (compounded semiannually)
i = r/m = 0.075/2 interest rate per period
t = 10 years
n = t*m = 10*2 = 20 total number of compounding periods
A = the future value (the amount in the account after t years)
A = P(1 + i)^n
A = 400*(1 + 0.075/2)^20
........
........
A = $835.26
If the compounding is done continuously we have:
r = 0.075 the rate as a decimal
A=Pe^(rt)
A = 400*e^(0.075*10)
........
........
A = $846.8
The 7.5% compounded continuously yields greater return.