# How to Calculate Compound Interest

Compound interest is interest which is calculated on the original lump sum plus the interest already accumulated.

If a lump sum (PV) is invested in an account paying a rate of compound interest (i), then after a number of periods (n), it will grow into a future value (FV).

Future value (FV) = Present Value (PV) + Compound Interest

This formula can be rearranged to give:

Compound Interest = Future value (FV) – Present Value (PV)

The compound interest can be found by taking the difference between the future value and the present value.

For example, is a lump sum of 10,000 is invested today in an account paying 8% a year compounded annually, then at the end of two years the future value is given by the as follows.

```PV = 10,000
i = 8%
n = 2
FV = PV x (1 + i)n
FV = 10,000 x (1 + 8%)2
FV = 11,664.00
```

and the compound interest is given by:

```Compound interest = FV - PV
Compound interest = 11,664 - 10,000
Compound interest = 1,664.00
```

This is presented in the diagram below

Difference between future values
Period 0 1 2 3
Future value 10,000 ↑ 11,664.00 ↑

### How to Calculate Compound Interest Between Two Periods

This same technique can be applied for any two periods.

Using the same example, if we wanted to know the compound interest earned for years 6,7,8 and 9, we calculate the future value at the end of year 5 (PV at the start of year 6), and the future value at the end of year 9 The difference between the two values must be the compound interest earned between year 6 and year 9.

Future value at year 5 (PV at the start of year 6) is given by:

```PV = 10,000
i = 8%
n = 5
FV = PV x (1 + i)n
FV = 10,000 x (1 + 8%)5
FV = 14,693.28
```

and, the future value at the end of year 9 is given by:

```PV = 10,000
i = 8%
n = 9
FV = PV x (1 + i)n
FV = 10,000 x (1 + 8%)9
FV = 19,990.05
```

and the compound interest earned for years 6, 7, 8, and 9 is given as follows:

```FV = FV at the end of year 9
PV = FV at the end of year 5 (PV at the start of year 6)
Compound interest = FV - PV
Compound interest = 19,990.05 - 14,693.28
Compound interest = 5,296.77
```

This is presented in the diagram below

Difference between future values
Period 5 6 7 8 9
Future value 14,693.28 ↑ 19,990.05 ↑

The compound interest between any two periods can be found by taking the difference between the future values at the start and end of the two periods. The future value can be calculated using the .

How to Calculate Compound Interest November 6th, 2016

## Related pages

gearing ratios definitionimprest cash bookjournal entry for unearned revenuenumber of days sales in receivables formulathe accounts receivable ledgerpetty cash balance sheetaccounting aptitude questions and answersbond issuance price calculatorcontinuously compounded ratefixed overhead volume variance formulapetty cash formatnominal annual rate of return formularequisition slip form sampleprepayment on balance sheetobsolete items in inventorycosting sheet templatehow to calculate annuity factorjournal entries for bank reconciliationdefine acid test ratiosunk cost accountingsubsidiary ledger vs general ledgermargin to markup conversionpresent value annuity table pdffob freight termsaccounts receivable turnover industry averagecashbook templatemandatorily redeemable preferred stocklifo examplesdefinition of source document in accountingpayroll tax accountant salaryebit coverageformula of material price variancewhat is pmt functioncash count spreadsheethow to calculate variable costinghow to calculate inventory conversion periodrecording accrued interestdepreciation calculation formulawhat is nsf checkaccounts payable balance sheet examplecomputation of deferred taxis accounts receivable debit or creditbank ledger templatepvad tableexample of cash flow statement analysismargin formula exceldaybook templatewhat is zero based budgeting definitionallowance for bad debt account typeinventory calculation in excelprinciple of bookkeepingaccounting system flowchart diagramhorizontal analysis of income statementbookkeeping tutorial philippinesppv accountingfob destination definitionconsignee account numberappropriation account for partnershipaccrued revenuesprofitability index rulequick ratio formula examplebad debts journal entriescreditor definition in accountinguses of standard costingcost of goods manufactured templatehow to find interest rate compounded continuouslydebit credit journalpresent worth exceldebit prepaid expenseexcel balance sheet formatprice and quantity variancesolved example of bank reconciliation statement