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Multiple Choice
What annual rate of return is earned on a $1 investment that grows to $1.21 in 2 years, compounded annually?
A
10%
B
21%
C
10\%
D
5%
Verified step by step guidance
1
Step 1: Understand the formula for compound interest. The formula to calculate the future value (FV) of an investment is: FV = PV × (1 + r)^n, where PV is the present value, r is the annual rate of return, and n is the number of compounding periods.
Step 2: Rearrange the formula to solve for the annual rate of return (r). The rearranged formula is: r = (FV / PV)^(1/n) - 1.
Step 3: Substitute the given values into the formula. Here, FV = $1.21, PV = $1, and n = 2 years. Plug these values into the formula: r = ($1.21 / $1)^(1/2) - 1.
Step 4: Simplify the fraction inside the parentheses. Divide FV by PV to get: r = (1.21)^(1/2) - 1.
Step 5: Interpret the result. The value of r represents the annual rate of return, expressed as a percentage. Ensure the calculation aligns with the compounding period (annually in this case).