your plan to retire exactly in 20 years.your goal is to create funds that will a
ID: 2729365 • Letter: Y
Question
your plan to retire exactly in 20 years.your goal is to create funds that will allow you to receive 20000 AT end of each year for 30 years between retirement and death based upon actuary tables.you know that you will be able to earn 11percent per year during the 30 years retirement period. (a)how large funds will you need when you retire in 20 years to provide 30 years 20000 retirement annuity. (b) how much will you need today as a single amount to provide the funds calculated in part. (c)above if you earn only 9 percent per year during 20 years preceding retirement.
Explanation / Answer
(a)how large funds will you need when you retire in 20 years to provide 30 years 20000 retirement annuity.
This is a present value of annuities problem.
The formula for PV of annuity:
PV = [C/i] * [1-1/{(1+i)n}]
Where C = annuity payments
i = interest
n = payment periods.
PV = [$20,000 / 11%] * [1-1/{(1+11%)30}]
PV = [$20,000 / 0.11] * [1-1/{(1+0.11)30}]
Therefore, PV = $173,875.85
(b) how much will you need today as a single amount to provide the funds calculated in part.
This will be a present value of principle problem. The formula for PV of principle:
PV = P / [(1+i)n]
Where P is the amount you want after n years at i interest
PV = $173,875.85 / [(1+11%)30]
PV = $173,875.85 / (1.11)30
PV = $173,875.85 / 22.89
PV = $7,596.15
(c)above if you earn only 9 percent per year during 20 years preceding retirement.
This will be a present value of principle problem. The formula for PV of principle:
PV = P / [(1+i)n]
Where P is the amount you want after n years at i interest
PV = $173,875.85 / [(1+.09)20]
PV = $31,024.82
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