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You inherited $225,000 from a rich uncle
You inherited $225,000 from a rich uncle. You have set yourself the objective of retiring in 30 years with at least $500,000 in savings. a) What is the minimum average annual rate you must earn to achieve that goal? b) After 20 years you are pleasantly surprised to find that your savings have grown into $400,000. What average rate did you earn for the first 20 years? Note: Both answers are annual rates. Express them as percentages.
Expert Solution
Future Value = Present Value * (1+r)^n
r = ?
n = 30 years
500,000 = 225,000 * (1+r)^30
(1+r)^30 = 500,000 / 225,000
(1+r)^30 = 2.22222222222
1+r = 2.22222222222^(1/30)
r = 1.02697431737 - 1
r = 2.70%
Now
Future Value = Present Value * (1+r)^n
r = ?
n = 20 years
500,000 = 225,000 * (1+r)^20
(1+r)^20 = 500,000 / 225,000
(1+r)^20 = 2.22222222222
1+r = 2.22222222222^(1/20)
r = 1.0407331168 - 1
r = 4.07%
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