Why timing matters
Money available today can be invested and earn a return, so a sum received today is worth more than the same sum received later. That single idea underpins almost every finance decision, from pricing a bond to approving a project.
Two operations move money through time. Compounding carries a present amount forward. Discounting brings a future amount back to today. They are the same relationship read in opposite directions.
Key points
- A taka today is worth more than a taka tomorrow.
- Compounding moves value forward; discounting moves it back.
- The rate and the timing must always describe the same period.
Compounding and discounting
FV = PV × (1 + r)ⁿ
Grows a present amount forward by a constant rate per period.
- PV
- Present value
- r
- Rate per period
- n
- Number of periods
PV = FV ÷ (1 + r)ⁿ
Brings a future amount back to today's value.
Use the same rate basis throughout. A monthly rate must pair with months, and an annual rate with years. Mixing the two is one of the most common sources of error.
When there are several cash flows, value each one separately and add the results. Later cash flows are discounted more heavily because they are further away.
A worked example
Suppose you invest ৳10,000 at a hypothetical 8% annual return. After one year it is worth ৳10,800. After two years it is ৳10,000 × 1.08² = ৳11,664.
Run the same relationship backwards. If you are promised ৳11,664 in two years and your required return is 8%, its present value is ৳11,664 ÷ 1.08² = ৳10,000. That is what the promise is worth to you today.
Where it shows up
Time-value arithmetic drives loan repayments, savings goals, pension funding, bond pricing, and every discounted cash flow model. In each case the structure is identical: a rate, a set of periods, and cash flows placed on the correct dates.
Keep compounding frequency and inflation explicit. Nominal cash flows belong with nominal rates, and real cash flows with real rates. Consistency matters more than any single formula.
Key points
- More distant cash flows are worth less today.
- Match the rate to the period of the cash flows.
- Nominal with nominal, real with real.
02 / Calculate
Watch value compound.
Change the starting amount, the rate, or the horizon. A negative rate models inflation and shows the loss of buying power.
An annual ৳100,000 grows at 8% for 15 years with no extra contributions.
Future value
৳317,216.91
After 15 years the balance is ৳3.17 L. You contributed ৳100,000.00 and earned ৳217,216.91 in growth.
Total interest earned
৳217,216.91
Compounding vs simple interest
+৳97,216.91
Year by year
| Year | Opening | Added | Growth | Closing |
|---|---|---|---|---|
| 1 | ৳100,000.00 | ৳0.00 | ৳8,000.00 | ৳108,000.00 |
| 2 | ৳108,000.00 | ৳0.00 | ৳8,640.00 | ৳116,640.00 |
| 3 | ৳116,640.00 | ৳0.00 | ৳9,331.20 | ৳125,971.20 |
| 4 | ৳125,971.20 | ৳0.00 | ৳10,077.70 | ৳136,048.90 |
| 5 | ৳136,048.90 | ৳0.00 | ৳10,883.91 | ৳146,932.81 |
| 6 | ৳146,932.81 | ৳0.00 | ৳11,754.62 | ৳158,687.43 |
| 7 | ৳158,687.43 | ৳0.00 | ৳12,694.99 | ৳171,382.43 |
| 8 | ৳171,382.43 | ৳0.00 | ৳13,710.59 | ৳185,093.02 |
| 9 | ৳185,093.02 | ৳0.00 | ৳14,807.44 | ৳199,900.46 |
| 10 | ৳199,900.46 | ৳0.00 | ৳15,992.04 | ৳215,892.50 |
| 11 | ৳215,892.50 | ৳0.00 | ৳17,271.40 | ৳233,163.90 |
| 12 | ৳233,163.90 | ৳0.00 | ৳18,653.11 | ৳251,817.01 |
| 13 | ৳251,817.01 | ৳0.00 | ৳20,145.36 | ৳271,962.37 |
| 14 | ৳271,962.37 | ৳0.00 | ৳21,756.99 | ৳293,719.36 |
| 15 | ৳293,719.36 | ৳0.00 | ৳23,497.55 | ৳317,216.91 |
Test the assumption
What if the rate changes?
The same inputs, compared across nearby rates.
6.0% rate
৳239,655.82
Comparison scenario
8.0% rate
৳317,216.91
Your current assumption
10.0% rate
৳417,724.82
Comparison scenario
Growth uses a constant annual rate with interest added once a year. Contributions are added at each year-end. Real products compound more often and carry fees, taxes, and risk.
03 / Apply
Funding a laptop in two years
A student needs ৳120,000 in two years and can earn an 8% annual return on savings. She wants to know how much to set aside today.
The assumptions
- The 8% return is a planning assumption, not a guarantee.
- No additional contributions are made during the two years.
- Interest compounds once a year.
What to take away
01
Discounting converts the goal into today's required amount.
02
A higher assumed return lowers the amount needed today, but adds risk.
Your turn
0 of 3 answered
01Question
At an 8% annual rate, what is ৳10,000 worth after 2 years? Round to the nearest taka.
02Question
What is the present value of ৳5,000 received in 3 years at a 6% annual rate? Round to two decimals.
03Question
Which change makes a future cash flow worth less today, holding the amount fixed?
Take it into the Lab
Experiment with the same idea.
The Lab turns this topic into a workspace: change the drivers, watch the statements move, and see the consequence before you commit to a decision.
What-if analysis
Change price, cost, and working capital. Watch margins, return, and risk move together.
Open the labFormula lab
Understand, manipulate, observe, solve, then apply the formula to a decision.
Walk the formulaStatement playground
See how one driver propagates through the income statement, balance sheet, and cash flow.
Open the playgroundSources & further reading
OpenStax · Principles of Finance (free textbook) ↗Educational sample content. Worked examples use hypothetical figures. Dates refer to the note's latest content update.