# Lump Sum Present and Future Value Formula

## The Time Value of Money

The time value of money concept in financial management is used to compare lump sum cash flows which are received or paid at different times.

The lump sum present and future value formulas can be used to calculate the effect of time and compounding interest rates on the value of the lump sums. They are best looked at by way of example.

###### From Present Value to Future Value of a Lump Sum

A lump sum received now and deposited at a compounding interest rate for a number of periods will have a future value.

If you have £100 and deposit it at 5%, after 1 year you would have £100 + 100 x 5% = £105, after 2 years you would have £105 + 105 x 5% = £110.25.

In this example, the £100 is the lump sum received now, the present value, and the £110.25 is the value in 2 years time at an interest rate of 5% and is called the future value.

###### From Future Value to Present Value of a Lump Sum

A lump sum received in the future and discounted back at a compounding interest rate (the money you would loose by not being able to invest it now) will have a present value.

If you receive £110.25 in 2 years time, and could have earned 5%, then in 1 years time the value of the lump sum would be £110.25 / 105% = £105. After 2 years the value of the lump sum would be £105 / 105% = £100.

In this example, the £110.25 is the future value of the lump sum, and the £100 is the present value of the lump sum at 5% for 2 years.

### Lump Sum Formulas

The following summarizes for easy reference the formulas for calculating present value of future payments, future value of lump sum, the compounding interest rate, and the number of periods of compounding. An example of using the lump sum formulas is given, together with the corresponding Excel formulas.

The formula to use will depend on which 3 of the 4 variables are already known.

In all present value and future value lump sum formulas the following symbols are used.

• FV means future value
• PV means present value
• i% is the period discount rate
• n is the number of periods
• LN is a natural logarithm
• * means multiply, and ^ means to the power of

The example used below for each of the annuity formulas is based on the following information.

• Future value = FV = £7,335.93
• Present value = PV = £4,622.88
• Period discount rate = i% = 8%
• Number of periods = n = 6

To Calculate the Future Value of a Lump Sum

 Formula FV  =  PV * (1 + i%)^n Example FV  = 4622.88 * (1 + 8%)^6 = 7,335.93 Excel Future Value Formula FV  =  – FV(i%,n,,PV)

To Calculate the Present Value of a Lump Sum

 Formula PV  =  FV / (1 + i%)^n Example PV  =  7,335.93 / (1 + 8%)^6 = 4,622.88 Excel Present Value Formula PV  =  – PV(i%,n,,FV)

The Find the Compounding Discount Rate

 Formula i  =  n√(FV / PV) – 1 Example i  =  (7335.93 / 4622.88)^(1 / 6)-1 = 8% Excel Interest Rate Formula i  =  RATE(n,,PV,- FV)

To find the Number of Periods

 Formula N  =  LN(FV / PV) / LN(1 + i%) Example N  =  LN(7,335.93/4,622.88)/LN(1+8%) = 6 Excel Periods Formula N  =  NPER(i%,,PV,- FV)

Lump Sum Present and Future Value Formula November 6th, 2016

## Related pages

calculate double declining balanceletter of credit accounting treatment ifrsbalance sheet vertical analysis exampleformula for diminishing value depreciationbookkeeping to trial balance examplesstock turnover periodis unearned revenue an assetannuity due calculatorexcel fv functionabbreviated accounts templateamortization straight line methodsmall business balance sheet template excelhow to calculate cost of goods sold in managerial accountingstockholders equity statement examplefactory overhead expensescalculate mark up percentagefreight in freight out accountingformula for profitability indexjournal entry of outstanding expensesdouble declining method exampleobjectivity principle accountingamortization bond premiumdays of sales outstanding formulaequity multiplier examplenet profit turnover ratio formulavariance analysis formula sheetadjusting entry for unearned rentsimple bookkeeping template for excelwhen is the unearned revenue recognized in the financial statementsgearing ratio analysis interpretationhow to calculate common size income statementirr of a perpetuityin a perpetual inventory systemfixed asset turnover ratio formula examplemulti step income statement template excelcalculate stockholders equityjob cost sheet formatbank account reconciliation templatedirect labor cost definitionsales ledger meaningtemplate for time sheetannuity forumlaperpetual periodic inventoryaverage cost inventory methodweighted average with percentagesdeferred revenue haircutlabor efficiency variancecash cheque definitionweighted average contribution margin per unitbond sinking fund balance sheethow to do fifo methodtreasury stock journal entryaccounting basics quizupdated cash book bank reconciliation statementlease calculator formulaexamples of accrualsis manufacturing overhead a fixed costwhat is controllable profitamortization template excelunder the allowance method writing off an uncollectible accountexcel formula for npvnet present value and profitability indextrial balance meaning in accountingbank to book reconciliation formatperiodic journal entriesbad debts written off journal entrydefinition of acid test ratioimpairment loss on intangible assetsaccounting ledgers examplesgaap journal entriespresent value of annuity due calculatordebtors formulajournal entry for accrued revenuesingle entry system of accounting formatbookkeeping spreadsheet template excel