Teaching companion · Time value of money

One dollar.
Six financial questions.

A monthly budget helps you choose what money needs to do now. The six functions of a dollar help you understand what happens across time.

Each function relates money at one date to money at another. Start with the question, identify what is known, then choose the function. These concepts support the Academy’s teaching; Ed directs classroom pacing and release.

Try the mathematics

What changes across time?

Start with the fictional $1,200 goal at 0% over 12 months, or enter your own assumptions. Figures are calculated in this browser and are not sent to the Academy. Calculator inputs are not saved when you leave.

Choose a financial question

Future goal, starting from zero ($)

Use US dollars, like 1250.50 or $1,250.50. Up to two decimal places; the tool does not round your entry.

Payment and compounding interval

Nominal annual rate (%)

Annual rate basis

Number of months

All recurring payments occur at period-end; the first is one full period from today. The rate stays fixed. Savings goals start with zero already saved. For monthly calculations, choose the rate basis stated in your source. The tool divides a nominal annual rate by 12, or converts an effective annual rate to an equivalent monthly rate. Annual intervals use the entered annual rate directly. Taxes, fees, inflation and issuer-specific daily-interest rules are excluded.

Deposit needed each period · monthly

$100.00

Starting with nothing already saved, a $1,200.00 goal over 12 months gives an estimated deposit of $100.00 at the end of each month.

This example assumes no interest (0%).

12 monthly periods · rate per period 0% · factor 0.083333333

Rate basis: nominal annual. Monthly decimal rate = annual decimal rate ÷ 12.

Amounts are rounded for display. Actual saving or repayment schedules may need a final adjustment. This is an educational estimate, not a bank balance, guaranteed return or lender quote.

To use a result in your plan, open My budget and expand “Plan a savings goal or loan payment.” Your figures are not placed in the link or transferred automatically.

Learn the question before the formula.

Key: PV = amount today; FV = amount at the future date; i = interest or discount rate per period, written as a decimal; n = number of periods; payment = equal amount each period.

Function 1

Future worth of $1

Also called: Compound amount of one

What can a single amount today become?

FV = PV × (1 + i)ⁿ

$1,000 today becomes $1,628.89 at the end of year 10.

Bring it to your budget. An existing reserve can grow over time. Keep the starting reserve separate from new monthly deposits.

Function 2

Future worth of $1 per period

Also called: Accumulation of one per period

What can regular equal deposits become?

FV = payment × [(1 + i)ⁿ − 1] ÷ i

$100 deposited at each year-end grows to $1,257.79 at the end of year 10. Total deposits: $1,000.

Bring it to your budget. A regular savings line in your budget supports a future goal. Deposit timing changes the outcome.

Function 3

Sinking fund factor

Also called: Periodic saving needed for a future goal

What regular deposit will reach a target?

payment = FV × i ÷ [(1 + i)ⁿ − 1]

To build $1,000 from a zero starting balance, set aside about $79.50 at each year-end for 10 years.

Bring it to your budget. Turn a future repair or replacement into a regular planned allocation. Update the target when costs change.

Function 4

Present worth of $1

Also called: Present value of one

What is one future amount worth today?

PV = FV ÷ (1 + i)ⁿ

$1,000 received at the end of year 10 has a present value of $613.91 at the assumed discount rate.

Bring it to your budget. Compare amounts at the same date. A future promise is not cash available to spend this month.

Function 5

Present worth of $1 per period

Also called: Present value of an ordinary annuity

What is a stream of equal future payments worth today?

PV = payment × [1 − (1 + i)⁻ⁿ] ÷ i

$100 received at each year-end for 10 years has a present value of $772.17.

Bring it to your budget. Look beyond the sum of installments when comparing payment arrangements. Consider their dates and all other terms.

Function 6

Periodic repayment

Also called: Capital recovery / installment to amortize one

What equal payment repays a loan?

payment = PV × i ÷ [1 − (1 + i)⁻ⁿ]

A $1,000 loan repaid over 10 years requires about $129.50 at each year-end.

Bring it to your budget. A debt payment includes principal and interest. Budget the contractual payment and verify lender terms before making changes.

From a future goal to this month’s plan.

Begin without assuming any interest: a $1,200 expense due in 12 months, with nothing already saved, calls for $100 each month. That is the sinking fund idea at 0%. Add that amount once to your budget’s savings or irregular-expense allocation, then check whether the plan balances.

For a monthly calculation, both the rate and the period count must be monthly. A nominal annual rate compounded monthly is divided by 12; an effective annual rate needs a different conversion: monthly rate = (1 + annual rate)^1/12 − 1. Actual loan disclosures and payment schedules govern; fees, daily interest and payment dates can change the result.

If i = 0, the formulas with division by i use their limits: a series accumulates to payment × n; its present value is payment × n; the payment for a target or loan is amount ÷ n. There is no interest growth at 0%.

Build my monthly budget →

Practice without sharing private figures.

Choose a fictional savings goal or loan. Mark today, the end date and every payment date.
Identify whether you have one amount or a series of amounts. Ask which of the six questions you need to answer.
State the rate, period count and payment timing. Work at 0% first, then explain how a positive rate changes the result.
For a monthly goal or repayment, carry the resulting payment into the appropriate budget row once. Annual amounts must be converted for a monthly plan; do not enter them as monthly payments.

Check your understanding

Building a future reserve from equal deposits uses future worth per period. Working backward from the reserve target to the needed deposit uses the sinking fund factor. Finding the payment on a loan uses periodic repayment. At 0%, saving $1,200 over 12 monthly deposits requires $100 per month.

One dollar.Six financial questions.