The formula PV x (1+r) = FV expresses the relationship between
A present and future value.
(B) risk and the value of money.
C discount rate and risk.
D liquidity and time.
E utility and value.
The correct answer and explanation is:
The correct answer is A) present and future value.
The formula PV×(1+r)=FV\text{PV} \times (1 + r) = \text{FV} expresses the relationship between present value (PV) and future value (FV). In this formula:
- PV (Present Value) is the current worth of a sum of money that you will receive or pay in the future, discounted by the interest rate over a specific period.
- FV (Future Value) is the amount of money you would have in the future, taking into account the interest earned over time.
- r represents the interest rate, typically expressed as a decimal. This is the rate at which the value of money increases over time.
The formula shows how the present value grows over time, based on the interest rate applied. For example, if you invest a sum of money today (PV) at a fixed interest rate (r), the amount of money you will have in the future (FV) can be calculated using this formula.
This equation is important in finance because it helps individuals and businesses determine how much a certain amount of money today is worth in the future, considering the time value of money. The time value of money concept holds that a specific amount of money today is worth more than the same amount in the future, due to the opportunity to earn interest or returns on that money.
In practical terms, this formula is used for various financial calculations such as investments, loans, savings, and retirement planning, as it helps determine the growth of money over time or the amount needed today to reach a future financial goal.