# Math

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Suppose an individual makes an initial investment of \$2400 in an account that earns 8%, compounded monthly, and makes additional contributions of \$100 at the end of each month for a period of 12 years. After these 12 years, this individual wants to make withdrawals at the end of each month for the next 5 years (so that the account balance will be reduced to \$0)

How much is in the account after the last deposit is made?

i used this Formula but wrong ?

A= R(1-(1+i)n0/i

• Math -

You are "moving" a single payment plus an annuity up on the time graph for 144 periods
i = .08/12 = .00666667

Amount at the end of 12 years
= 2400(1.00666667)^144 + 100(1.00666667^144 - 1)/.00666667
= 6248.134 + 24050.841
= 30298.98

If you want the monthly withdrawals for the next 5 years, let that withdrawal be x

30298.975 = x( 1 - 1.0066667^-60)/.0066667
x = 614.35

• Math -

tks so much

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