# Explain compounding technique in the time value of money.

If the interest is compounded, that means the interest which is earned at the end of year, will be added to principal and will go on till the end of time. Future values are calculated by using this compounding interest.

As interest rates increases, compounding interest also increases, that means if you want large sum of money, interest rates must be high. So, when investors were investing, they should look for higher interest rate to get high returns in this method.

Basic compounding problems includes −

• Future value of a single sum: compounds single amount to future value

• Future value of a series of payments: compounds annuity to a future values.

• Payments needed to achieve a future value: compound series of equal payments into future value.

## Formula

• General formula

FVn = PV (1+r) ^n

Where,

1+r = future value interest factor

PV = initial cash flow

r = rate of interest

n = number of years

FVn = future value @nth year

• FV of a lump sum

FVn = PV (1+r) ^n

• Multiple compounding

FVn = PV (1+(r/m)) ^m*n

m = No. of times compounding (during a year)

n = No. of years in which compounding is done

• Future value for multiple cash flows

FVn = PV (1+ (r/m))

• Effective rate of interest (EIR) for multiple period compounding

EIR = (1+ (r/m)) ^m – 1

r = yearly interest rate, m = frequency of compounding per year.