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Multiple Choice
Which of the following is the equivalent of \$300 received today, if the annual interest rate is 5\% compounded annually and the amount is to be received in 2 years?
A
\$300 \(\div\) (1 + 0.05)^2 = \$272.11
B
\$300 \(\times\) (1 - 0.05)^2 = \$270.75
C
\$300 \(\div\) (1 - 0.05)^2 = \$332.64
D
\$300 \(\times\) (1 + 0.05)^2 = \$330.75
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Verified step by step guidance
1
Understand the concept of future value (FV) and present value (PV). Future value is the amount of money an investment will grow to over a period of time at a specified interest rate. Present value is the current worth of a future sum of money given a specific interest rate.
Identify the formula for future value with annual compounding: FV = PV × (1 + r)^n, where PV is the present value, r is the annual interest rate, and n is the number of years.
Substitute the given values into the formula: PV = \$300, r = 0.05 (5%), and n = 2 years. The formula becomes FV = 300 × (1 + 0.05)^2.
Perform the calculation step-by-step: First, calculate (1 + 0.05), which equals 1.05. Then, raise 1.05 to the power of 2 (1.05^2). Finally, multiply the result by 300.
Compare the calculated future value to the options provided in the problem to determine the correct answer.