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Compounding and Discount Factors Calculator

Future value equals present value times one plus interest rate raised to the power of n

Solution

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Single Payment Compound Amount

Calculates the future value of a single lump-sum investment compounded at a fixed interest rate over n periods.

F = P(1+i)ⁿ

Single Payment Present Worth

Discounts a future lump sum back to its present value at a given interest rate.

P = F / (1+i)ⁿ

Capital Recovery

Converts a present amount into equal annual payments over n periods. Used for loan amortization.

A = P × i(1+i)ⁿ / [(1+i)ⁿ − 1]

Uniform Series Compound Amount

Calculates the future value of a series of equal annual deposits with compound interest.

F = A × [(1+i)ⁿ − 1] / i

Uniform Series Present Worth

Calculates the present value of a series of equal annual payments.

P = A × [(1+i)ⁿ − 1] / [i(1+i)ⁿ]

Uniform Series Sinking Fund

Determines the equal annual deposit needed to accumulate a target future amount.

A = F × i / [(1+i)ⁿ − 1]

How It Works

Discrete compounding discount factors quantify how money grows or shrinks over time at a fixed interest rate. The six equations cover every standard relationship between a present sum (P), a future sum (F), and equal periodic payments (A). Single payment factors handle lump sums. Uniform series factors handle equal annual deposits or withdrawals. Capital recovery converts a present investment into an equivalent annuity, while the sinking fund converts a future goal into required periodic savings.

Example Problem

You invest $1,000 today at 5% annual interest for 5 years. What is the future value?

  1. F = $1,000 × (1 + 0.05)⁵
  2. F = $1,000 × 1.27628 = $1,276.28

Capital Recovery: borrowing $1,000 at 5% for 5 years requires annual payments of A = $230.97.

Key Concepts

The six discrete compounding factors cover every standard time-value-of-money relationship between a present sum (P), a future sum (F), and equal periodic payments (A). Single-payment factors handle lump sums growing or being discounted over time. Uniform-series factors handle equal periodic cash flows. Capital recovery converts a present amount into an equivalent annuity (loan payments), while the sinking fund converts a future goal into required periodic savings.

Applications

  • Loan amortization: calculating monthly or annual payments to repay a mortgage or car loan
  • Retirement planning: determining how much to save annually to reach a target nest egg
  • Project evaluation: discounting future cash flows to present value for NPV analysis
  • Bond pricing: computing the present worth of a bond's coupon payments and face value
  • Equipment leasing: finding the annual cost equivalent of purchasing capital equipment

Common Mistakes

  • Entering interest rate as a percentage instead of a decimal — enter 0.05 for 5%, not 5
  • Confusing capital recovery with sinking fund — capital recovery starts from a present amount (P→A), sinking fund targets a future amount (F→A)
  • Using the wrong number of periods — monthly payments require monthly interest rate and total months, not annual rate and years
  • Ignoring the sign convention — cash inflows and outflows should be consistent; mixing signs gives meaningless results

Frequently Asked Questions

What is the time value of money?

Money available today is worth more than the same amount in the future because it can earn interest. A $1,000 investment at 5% becomes $1,050 after one year. Compounding factors quantify this growth precisely.

What is the difference between capital recovery and sinking fund?

Capital recovery finds the equal annual payment needed to repay a present loan amount (P to A). A sinking fund finds the equal annual deposit needed to accumulate a future target amount (F to A). Both use the same interest rate and period count but work in opposite directions.

When should I use single payment vs. uniform series?

Use the single payment factor for lump-sum investments or one-time payments. Use the uniform series factor for regular deposits or withdrawals, such as contributing $200/month to a retirement account.

How does the number of periods affect compounding?

More periods mean more compounding cycles and greater growth. At 7% interest, $10,000 grows to $19,672 in 10 years but $38,697 in 20 years. The doubling effect accelerates over longer horizons.

Why enter interest rate as a decimal?

Engineering economics convention uses the decimal form directly in formulas. Enter 0.05 for 5%, 0.12 for 12%, etc. This avoids ambiguity between percentage and decimal forms in multi-step calculations.

Reference: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.

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