Question

Find the amount of each annuity A) after 12 monthly deposits of $200 at 5% compounded monthly B) after 5 annual deposits of $1000 at 3% compounded annually.

Answer 1

SOLUTION:

From given data,

Find the amount of each annuity

To find withdraw amount we will use following formula:

PV=C*[ ( 1−(1+i)^−n) / i]

PV = Initial deposit
C = Regular withdraw amount
i = Interest rate per period
n = number of periods

A) after 12 monthly deposits of $200 at 5% compounded monthly

the number of periods is n=12,

the interest rate per period is i=0.05,

the initial deposit is PV=200.

After substituting the values into the formula we have:

PV=C*[ ( 1−(1+i)^−n) / i]

200 =C*[ ( 1−(1+0.05)^−12) / 0.05]

200 =C*[ ( 1−1.05^−12) / 0.05]

200 =C*[ ( 1−0.556837) / 0.05]

200 =C*8.86326

C = 200 / 8.86326

C = 22.57

The amount you can withdraw every month is $ 22.57

B) after 5 annual deposits of $1000 at 3% compounded annually.

the number of periods is n=5 years⋅12=60

the interest rate per period is i=0.0312=0.0025

the initial deposit is PV=1000

After substituting the values into the formula we have:

PV=C*[ ( 1−(1+i)^−n) / i]

1000 =C*[ ( 1−(1+0.0025)^−60) / 0.0025]

1000=C*[ ( 1−1.0025^−60) / 0.0025]

1000=C*[ ( 1−0.860869) / 0.0025]

1000 =C*55.6524

C = 1000/ 55.6524

C = 17.97

The amount you can withdraw every month is $ 17.97

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