Problema Solution
A person who invests $1200 each year finds one choice that is expected to pay 9 percent per year and another choice that may pay 10 percent. What is the difference in return if the investment is made for 15 years?
Answer provided by our tutors
P = $1,200
r1 = 0.09 or 9%
r2 = 0.10 or 10%
t = 15 years
The formula for the return (profit or interest earned) after t years is:
I = P((1 + r)^t - 1), where r is the interest rate
For r1 = 0.09 or 9% we have:
I1 = P((1 + r1)^t - 1)
I1 = 1200((1 + 0.09)^15 - 1)
I2 = P((1 + r2)^t - 1)
I2 = 1200((1 + 0.10)^15 - 1)
I2 - I1 = 1200((1 + 0.10)^15 - 1 - (1 + 0.09)^15 + 1) = 1200(1.10^15 - 1.09^15) = $641.72
The difference in the return is $641.17.