TVM Basics
This concept explains why a dollar today is worth more than a dollar received in the future.
What is the Time Value of Money?
Explanation: Money today can be invested and earn interest, so receiving money today is generally more valuable than receiving the same amount later.
This represents what an investment made today will be worth at some point in the future.
What is Future Value?
Explanation: Future Value, or FV, is the amount an investment grows to after one or more periods at a given interest rate.
This represents what a future amount of money is worth today.
What is Present Value?
Explanation: Present Value, or PV, is the current value of future cash flows.
On a financial calculator, this button represents the number of periods.
What is N?
Explanation: N represents the number of periods in a TVM calculation.
If you know PV, FV, and the number of periods, you can solve for this variable to determine the investment’s return.
What is the Interest Rate?
Explanation: Chapter 4 teaches students to solve for r, the rate of return or interest rate.
The original amount of money invested is known as this.
What is the Principal?
Explanation: The principal is the starting amount of an investment before interest is earned.
In the formula FV = PV(1 + r)^t, this variable represents the number of periods.
What is t?
Explanation:
FV = PV(1 + r)^t
Finding the Present Value of a future cash flow is known as this.
What is Discounting?
Explanation: Discounting is essentially the reverse of compounding.
With compounding, we move money forward in time.
With discounting, we move money back toward today.
On a financial calculator, this button is used to enter the interest rate.
What is I/Y?
Explanation: I/Y is the interest rate per period when the calculator is properly configured.
On the financial calculator, after entering PV, FV, and N, you use CPT followed by this button to solve for the interest rate.
What is I/Y?
Explanation: The calculator process is:
Enter PV
Enter FV
Enter N
CPT → I/Y
Interest earned only on the original principal is called this.
What is Simple Interest?
Explanation: Simple interest only earns interest on the original amount invested.
You invest $100 for one year at 10%. The Future Value after one year is this.
What is $110?
Explanation:
FV = $100(1.10)
FV = $110
Complete the Present Value formula: PV = FV divided by this.
What is (1 + r)^t?
Explanation:
PV = FV ÷ (1 + r)^t
You divide the future amount by the appropriate discount factor.
When entering an 8% interest rate into the financial calculator, you enter this number instead of .08.
What is 8?
Explanation: On the BA II Plus, interest rates are entered as percentages.
So:
8% → enter 8
NOT:
8% → enter .08
$100 grows to $133.10 in three years. The annual interest rate is this.
What is 10%?
Explanation:
$100 growing at 10%:
Year 1 = $110
Year 2 = $121
Year 3 = $133.10
Interest earned on both the original principal and previously earned interest is called this.
What is Compound Interest?
Explanation: Compounding creates interest on interest.
For example, $100 invested at 10% becomes $110 after one year, and in the second year interest is earned on the entire $110.
You invest $100 at 10% for two years. With compounding, the Future Value is this.
What is $121?
Explanation:
FV = $100(1.10)²
FV = $121
The second year earns interest on both the original $100 and the interest earned during Year 1.
You will receive $121 two years from now. If the interest rate is 10%, the Present Value is this.
What is $100?
Explanation:
PV = $121 ÷ (1.10)²
PV = $121 ÷ 1.21
PV = $100
Before beginning a new Time Value of Money problem, you should use this calculator command to remove the previous problem’s values.
What is CLR TVM?
Explanation: The slides specifically remind students to clear the TVM registers before each problem so old values do not accidentally carry over.
This shortcut estimates how many years it will take an investment to double.
What is the Rule of 72?
Explanation: The Rule of 72 estimates doubling time:
Years to Double ≈ 72 ÷ Interest Rate (%)
$100 invested at 10% for two years grows to $121 with compound interest. The extra $1 compared with simple interest comes from this.
What is interest on interest?
Explanation: With simple interest, the ending amount would be $120. With compounding, the first year’s $10 of interest also earns 10%, creating another $1.
Holding everything else constant, increasing either the interest rate or the number of periods will have this effect on Future Value.
What is increase Future Value?
Explanation: The Chapter 4 relationship is:
More time = Higher FV
Higher rate = Higher FV
Holding Future Value constant, increasing either the interest rate or the amount of time will have this effect on Present Value.
What is decrease Present Value?
Explanation: The Chapter 4 relationships are:
More time = Lower PV
Higher rate = Lower PV
When entering PV and FV into a financial calculator, one should generally be positive and the other should be this.
What is negative?
Explanation: The calculator follows the cash-flow sign convention:
Positive = Cash Inflow
Negative = Cash Outflow
For example, if you invest $100 today:
PV = -100
The money you receive later is positive. If PV and FV have the same sign when solving for some variables, the calculator may return Error 5 or No Solution
Using the Rule of 72, an investment earning 8% per year will take approximately this many years to double.
What is 9 years?
Explanation:
72 ÷ 8 = 9 years
The Rule of 72 gives an approximation, not an exact answer. Your Chapter 4 slides note it is intended for rates in roughly the 5% to 20% range.