Multiple Choice
Which one of the following formulas correctly defines the Rule of 72 for estimating the number of years required to double an investment at a given annual interest rate?
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10. Time Value of Money
Time Value of Money Equations
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Which equation best represents the calculation of future value (\(FV\)) using simple interest?
A
\(FV = PV \times (1 + r)^t\)
B
\(FV = PV \times (1 + rt)\)
C
\(FV = PV \div (1 + rt)\)
D
\(FV = PV + (PV \times r \times t^2)\)
Verified step by step guidance1
Step 1: Understand the concept of simple interest. Simple interest is calculated on the principal amount (
MathML: PV
) over a period of time (
MathML: t
) at a fixed interest rate (
MathML: r
). The formula for simple interest is
MathML: Interest = PV × r × t .
Step 2: Recognize that the future value (
MathML: FV
) is the sum of the principal amount (
MathML: PV
) and the interest earned. Therefore, the formula for future value using simple interest is
MathML: FV = PV + (PV × r × t ).
Step 3: Simplify the formula for future value. Factor out
MathML: PV
from the equation:
MathML: FV = PV × (1 + r × t ).
Step 4: Compare the simplified formula (
MathML: FV = PV × (1 + r × t )
) with the options provided in the problem. This matches the correct answer.
Step 5: Note that other options provided in the problem do not align with the principles of simple interest. For example,
MathML: FV = PV × (1 + r )t
represents compound interest, and
MathML: FV = PV ÷ (1 + r × t )
is not a valid formula for future value.
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