# Annuity (finance Theory) - Example Calculations

Example Calculations

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

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

Examples:

1. 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
2. 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:

1. 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
2. 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

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