Future value calculations involve:
a. discounting.
b. add-on interest.
c. simple interest.
d. compounding
e. an annuity.
ii) When prices are rising at a rate of 3 percent, the cost of products and services would double in years.
a. 3
b. 18
c. 72
d. 6
e. 24
The correct answer and explanation is:
Question 1: Future Value Calculations
The correct answer is: d. compounding
Explanation:
Future value calculations involve determining how much an investment made today will grow to at a specific point in the future, assuming a certain rate of return or interest. This process is based on compounding, which means reinvesting the earned interest so that future interest is calculated on both the principal amount and the previously earned interest.
Compounding is key in future value calculations because it recognizes the time value of money, which states that money today is worth more than the same amount in the future due to its earning potential. The formula for future value (FV) under compounding is: FV=PV×(1+r)nFV = PV \times (1 + r)^n
where:
- PVPV is the present value (initial investment),
- rr is the interest rate per period, and
- nn is the number of compounding periods.
By contrast:
- Discounting is the opposite of compounding, used in present value calculations.
- Simple interest does not reinvest interest.
- Add-on interest is typically used in loans but doesn’t consider compounding.
- Annuities involve equal periodic payments rather than single investments.
Question 2: Doubling Time with a 3% Inflation Rate
The correct answer is: e. 24
Explanation:
To calculate how long it takes for prices to double given an annual inflation rate, we use the Rule of 72. This rule provides a quick estimate by dividing 72 by the annual rate of inflation: Doubling time=72Annual inflation rate (%)\text{Doubling time} = \frac{72}{\text{Annual inflation rate (\%)}}
For an inflation rate of 3%: Doubling time=723=24 years.\text{Doubling time} = \frac{72}{3} = 24 \text{ years.}
The Rule of 72 works because of logarithmic relationships between growth rates and time in compounding scenarios. It provides a straightforward way to approximate how long it takes for money or prices to double under a fixed growth or inflation rate. At 3% inflation, the cost of goods and services will double in approximately 24 years, reducing the purchasing power of money significantly.