Final answer:
To find the future value of an investment adjusted for inflation, subtract the annual inflation rate from the annual return rate and apply the resulting rate to the compound interest formula. The typo in the provided annual return rate (496) is acknowledged and assumed to be 4.96% for calculation purposes. Correctly adjusted future value can be found using the formula $10,000(1 + adjusted rate)^3, choosing the closest given option as the answer. Therefore correct option is E
Step-by-step explanation:
To calculate the future value of an investment adjusted for inflation, we need to account for both the rate of return on the investment and the rate of inflation.
The question involves finding the approximate future value, in actual dollars, of $10,000 invested today with an annual inflation rate (i) of 2% and an effective annual return on investment (r) of 496, which appears to be a typo and should possibly represent 4.96% or some similar, reasonable rate.
Let's proceed assuming an effective annual return (r) of 4.96% over three years.
To find the future value of the investment, we use the formula for compound interest:
FV = P(1 + r)^n, where:
FV = future value,
P = principal amount (initial investment),
r = annual return rate,
n = number of years.
First, we calculate the future value without inflation:
FV = $10,000(1 + 0.0496)^3.
However, to adjust for inflation, we must also take into account the purchasing power of the money in future years. We can adjust the annual return rate by subtracting the inflation rate:
Adjusted return rate = r - i = 4.96% - 2% = 2.96%.
Now, using the adjusted return rate, we calculate the future value adjusted for inflation:
FV adjusted = $10,000(1 + 0.0296)^3.
= 10914
Ten thousand dollars is invested today. If the annual inflation rate () is 2% and the effective annual return on investment (constant dollars) () is 496, what will be the approximate future value of the investment, adjusted for inflation (actual dollars), in three years?
Select one:
a. $10,236
b. $9,784
c. $11,937
d. $12,415
e. $10914