Suppose an initial deposit of D dollars into a savings account yielding p% per y

Question

Suppose an initial deposit of D dollars into a savings account yielding p% per year. We would like to know how much capital a person needs to initially deposit when he/she retires to live for N years. How much money needs to be initially deposited to last exactly N years when withdrawing W dollars per.war (starting after the first year) out of the account? [Note: the partial sum of a geometric series is given by: sigma^N_i=1 b r^i - 1 = b(1 - r^N)/(1 - r)]. In a realistic scenario, the average person retires at 65 and the life expectancy is about 80 years. Assume p = 5% a year and that the person needs 30,000 per year to sustain themselves. How much does this person need to invest at retirement? Compare this to the total amount needed to live for 15 years at 30,000 per year (= 15 Times 30,000 = 450,000).

Explanation / Answer

Solution:

Average person retiresa t 65 expected to live 80 years interest 5% need 30,000 for 15 years hence how much needs to invest at 65 years

Solution 3:

hence the total amount needed to live would be 45000 but need to invest 311389 hence the amount earn extra in 15 years is the interest earned and which is $138610

Year CAsh flow Discount 5% Cash flow present value 1 30000 0.952 28571.43 2 30000 0.907 27210.88 3 30000 0.864 25915.13 4 30000 0.823 24681.07 5 30000 0.784 23505.78 6 30000 0.746 22386.46 7 30000 0.711 21320.44 8 30000 0.677 20305.18 9 30000 0.645 19338.27 10 30000 0.614 18417.40 11 30000 0.585 17540.38 12 30000 0.557 16705.12 13 30000 0.530 15909.64 14 30000 0.505 15152.04 15 30000 0.481 14430.51 Should be the total investment made today 311389.74

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