Compare the accumulated value of an IRA account into which $500 is invested at t

Question

Compare the accumulated value of an IRA account into which $500 is invested at the end of each month; the account earns 2.5% annual interest. Make sure you compare how much was invested and how much interest was earned.

a.       You start at age 25 and retire at 60.

b.       You start at age 30 and retire at 60.

c.        You start at age 35 and retire at 60.

d.       You start at age 40 and retire at 60.

The questions should be answered with a table created in excel. Make sure the column headings are clearly labeled and use appropriate units.

Explanation / Answer

We can calculate the future value of annuity i.e. value of investment using following formula, FV of annuity = P * {[(1+r)^n - 1]/r} FV of annuity = Future value of annuity P = Monthly payment r = rate of interest per month n = number of months Answer a FV of annuity = Future value of annuity =? P = Monthly payment = $500 r = rate of interest per month = 2.5%/12 = 0.002083 n = number of months = 35 years * 12 = 420 FV of annuity = 500 * {[(1+0.002983)^420 - 1]/0.002083} FV of annuity = 500 * 670.4126 FV of annuity = 335206.28 Value of investment at the end of 60th year = $3,35,206.28 Answer b FV of annuity = Future value of annuity =? P = Monthly payment = $500 r = rate of interest per month = 2.5%/12 = 0.002083 n = number of months = 30 years * 12 = 360 FV of annuity = 500 * {[(1+0.002983)^360 - 1]/0.002083} FV of annuity = 500 * 535.3675 FV of annuity = 267683.77 Value of investment at the end of 60th year = $2,67,683.77 Answer c FV of annuity = Future value of annuity =? P = Monthly payment = $500 r = rate of interest per month = 2.5%/12 = 0.002083 n = number of months = 25 years * 12 = 300 FV of annuity = 500 * {[(1+0.002983)^300 - 1]/0.002083} FV of annuity = 500 * 416.1752 FV of annuity = 208087.62 Value of investment at the end of 60th year = $2,08,087.62 Answer d FV of annuity = Future value of annuity =? P = Monthly payment = $500 r = rate of interest per month = 2.5%/12 = 0.002083 n = number of months = 20 years * 12 = 240 FV of annuity = 500 * {[(1+0.002983)^240 - 1]/0.002083} FV of annuity = 500 * 310.9747 FV of annuity = 155487.35 Value of investment at the end of 60th year = $1,55,487.35 Option Invested amount Value of investment at the end of 60 th year Interest Earned A B C C-B a $210,000.00 $335,206.28 $125,206.28 b $180,000.00 $267,683.77 $87,683.77 c $150,000.00 $208,087.62 $58,087.62 d $120,000.00 $155,487.35 $35,487.35

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