Financial Calculus: Time Value of Money, Accumulation, and Discounting

Fill-in-the-blank practice flashcards covering fundamental financial calculus concepts, including the time value of money, accumulation, discounting, conjugate factors, and annual interest and discount rates.

Financial calculus is the mathematics of comparing money available at __________ in time.

different points

The principle stating that identical numerical amounts at different dates are not financially equivalent due to interest, risk, and opportunity cost is called the __________.

Time Value of Money (TVM)

The initial amount of money invested or lent is called the __________, initial capital, or present value.

principal

The total amount obtained at a future date, including the original capital and the interest earned, is called the __________ amount.

accumulated

The date on which a payment becomes due is called the __________.

maturity

In an investment such as a __________, the return is normally received at maturity rather than through periodic interest payments.

zero-coupon bond

Under the commercial (or financial) year convention, a year is assumed to have __________ days consisting of 12 months of 30 days.

$$360$$

On a financial timeline, a minus sign indicates money paid, whereas a plus sign indicates money __________.

received

Accumulation determines how much money invested today will be worth in the future, while discounting determines how much a future payment is worth __________.

today

The accumulation factor $f(t)$, which indicates how much one unit of money grows into over a period, is defined by the formula $f(t) = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$\frac{A}{P}$$

The discount factor $\phi(t)$, which represents the present value of each unit of currency payable in the future, is defined as $\phi(t) = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$\frac{P}{N}$$

The discount $D$ is the difference between the future nominal amount and its present value, given by $D = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$N - P$$

Interest is measured relative to the initial capital, whereas discount is measured relative to the __________ amount.

future

In terms of interest earned $I$ and initial capital $P$, the accumulation factor can be expressed additively as $f(t) = 1 + \text{\_\_\_\_\_\_\_\_\_\_}$.

$$\frac{I}{P}$$

In terms of discount $D$ and future nominal amount $N$, the discount factor can be expressed additively as $\phi(t) = 1 - \text{\_\_\_\_\_\_\_\_\_\_}$.

$$\frac{D}{N}$$

Two factors are called financially conjugate when their product equals $1$, represented by the relationship $f(t) \cdot \phi(t) = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$1$$

The annual interest rate $i$ measures the interest earned over one year relative to the initial capital, yielding the accumulated amount formula $A = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$P(1 + i)$$

The annual discount rate $d$ measures the discount over one year relative to the future amount, yielding the present value formula $P = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$N(1 - d)$$

Expressed in terms of the annual discount rate $d$, the one-year discount factor is $\phi(1) = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$1 - d$$