THE LEARNING LAB / FREE TO EVERYONE

Make time and
cash flow visible.

Explore a lump sum, regular savings, a target fund, an annuity due, and a perpetuity from one transparent set of assumptions. The calculation happens on the server and the form is not saved to your account or browser.

Working assumptions

The return is an effective annual assumption. Use payment dates per year to model monthly, quarterly, annual or another regular cash-flow rhythm. All outputs are illustrative and retain full precision before display rounding.

120 PAYMENT PERIODS / 10 YEARS

Future value, end-of-period contributionsKES 2,017,135
Future value, beginning-of-period contributionsKES 2,028,724
Present value of the stated targetKES 926,387
Required end-of-period sinking-fund contributionKES 9,905

Choose the relationship that fits the decision.

RelationshipResultPractical use
Future value of a lump sumKES 215,892What an amount already invested could become.
Future value, ordinary annuityKES 1,801,243Savings paid at the end of each month, quarter or year.
Future value, annuity dueKES 1,812,832Contributions made at the beginning of each period, such as rent or a pre-funded savings instruction.
Present value, ordinary annuityKES 834,324Today’s value of a known stream paid at each period-end.
Present value, annuity dueKES 839,692Today’s value when the first cash flow arrives immediately.
Required annuity-due sinking-fund contributionKES 9,842How much to set aside at each period-start to meet the stated future goal.

Perpetuity view

Level perpetuity valueKES 1,500,000
Growing perpetuity valueKES 1,500,000

The level value assumes the stated annual cash flow continues indefinitely without growth. Perpetuity outputs are useful for understanding long-lived income streams and terminal-value logic, but they are especially sensitive to the discount-rate and growth assumptions.

Follow the calculation.

Formulae used
\[ i = (1+r)^{1/m} - 1, \qquad n = m \times t \]

Periodic rate equals the effective annual rate converted to the selected payment frequency; periods equal payment dates per year times years.

\[ FV_{\text{ordinary}} = PMT \times \frac{(1+i)^n - 1}{i}, \qquad FV_{\text{due}} = FV_{\text{ordinary}}(1+i) \]

Future value of an ordinary annuity adds payments at each period-end. An annuity due moves each payment one period earlier.

\[ PV_{\text{ordinary}} = PMT \times \frac{1-(1+i)^{-n}}{i}, \qquad PV_{\text{due}} = PV_{\text{ordinary}}(1+i) \]

Present value discounts a regular stream back to today. An annuity due has one more period of value.

\[ PMT_{\text{sinking}} = \frac{G - PV(1+i)^n}{\frac{(1+i)^n - 1}{i}}, \qquad PV_{\text{perpetuity}} = \frac{C_1}{r-g} \]

A sinking fund solves for the regular amount needed to meet a target. A growing perpetuity is valid only when the discount rate is greater than long-run growth.

When the periodic rate is zero, the annuity factors become the number of payment periods. The calculator handles that case directly rather than dividing by zero.

Change the rate, not the story.

Only the effective annual return changes in these three scenarios. Regular contribution, target, inflation and time stay the same.

Effective annual returnFuture value, ordinary contributionsIn today’s purchasing power
6.00%KES 1,803,819KES 1,107,389
8.00%KES 2,017,135KES 1,238,346
10.00%KES 2,258,013KES 1,386,224
Inspect each year
YearTotal cash contributedEnd-of-period contributionsBeginning-of-period contributionsOrdinary result in today’s KES
1KES 220,000KES 232,339KES 233,139KES 221,275
2KES 340,000KES 375,265KES 376,929KES 340,376
3KES 460,000KES 529,625KES 532,222KES 457,510
4KES 580,000KES 696,334KES 699,939KES 572,875
5KES 700,000KES 876,379KES 881,073KES 686,666
6KES 820,000KES 1,070,829KES 1,076,697KES 799,069
7KES 940,000KES 1,280,834KES 1,287,972KES 910,265
8KES 1,060,000KES 1,507,639KES 1,516,149KES 1,020,430
9KES 1,180,000KES 1,752,589KES 1,762,579KES 1,129,735
10KES 1,300,000KES 2,017,135KES 2,028,724KES 1,238,346

Use a schedule when the obligation is a loan.

The mortgage planner models a repayment schedule, interest split, final balance, and the effect of an extra monthly payment. Use the companion workbooks for variable rates, irregular cash flows, tax, and full scenario analysis.

Open the loan repayment planner →

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Give the numbers
some context.

Get research notes and worked examples that build on the relationships explored here.