Question

1-Calculating Annuity Future Values. You are planning to make monthly deposits of $475 into a retirement account that pays 10 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 30 years?

2-Calculating Annuity Future Values. In the previous problem, suppose you make $5,700 annual deposits into the same retirement account. How large will your account balance be in 30 years?

Answer 1

Answer : 1) Calculation of Future Value of Annuity :

Future Value of Annuity = Periodic Payment * {[(1+r)^n - 1] / r }

where

r is the rate of interest per period i.e 10%/12 or 0.833333% or 0.008333333

n is the number of payments i.e 30 * 12 = 360

Periodic Payment is $475

Future Value = 475 * {[(1+0.00833333)^360 - 1] / 0.00833333 }

= 475 * {[19.837399 - 1] /0.00833333 }

= 475 * { 18.837399 / 0.00833333 }

= 475 * 2260.4879

= 1073731.76

2-) Calculation of Future Value of Annuity

First calculate Effective Annual rate

Effective Annual Rate = [1 + (Rate/number of compounding period)]^number of compounding period - 1

= [1 + (0.10 / 12)]^12 - 1

= 10.4713% or 0.104713

r is the rate of interest per period i.e 0.104713

n is the number of payments i.e 30

Periodic Payment is $5700

Future Value = 5700 * {[(1+0.104713)^30 - 1] / 0.104713 }

= 5700 * {[19.837399 - 1] /0.104713}

= 5700 * { 18.837399 / 0.104713 }

= 5700 * 179.895402

= 1025403.79