**Example Calculations**

Formula for Finding the Periodic payment(R), Given A:

R = A/(1+〖(1-(1+(j/m) )〗^(-(n-1))/(j/m))

Examples:

- Find the periodic payment of an annuity due of $70000, payable annually for 3 years at 15% compounded annually.
- R = 70000/(1+〖(1-(1+((.15)/1) )〗^(-(3-1))/((.15)/1))
- R = 70000/2.625708885
- R = $26659.46724

- Find the periodic payment of an annuity due of $250700, payable quarterly for 8 years at 5% compounded quarterly.
- R= 250700/(1+〖(1-(1+((.05)/4) )〗^(-(32-1))/((.05)/4))
- R = 250700/26.5692901
- R = $9435.71

Finding the Periodic Payment(R), Given S:

R = S,/((〖((1+(j/m) )〗^(n+1)-1)/(j/m)-1)

Examples:

- Find the periodic payment of an accumulated value of $55000, payable monthly for 3 years at 15% compounded monthly.
- R=55000/((〖((1+((.15)/12) )〗^(36+1)-1)/((.15)/12)-1)
- R = 55000/45.67944932
- R = $1204.04

- Find the periodic payment of an accumulated value of $1600000, payable annually for 3 years at 9% compounded annually.
- R=1600000/((〖((1+((.09)/1) )〗^(3+1)-1)/((.09)/1)-1)
- R = 1600000/3.573129
- R = $447786.80

Read more about this topic: Annuity (finance Theory)

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