At 20 years old, Josh is an avid saver. He wants to put an equalamount...

At 20 years old, Josh is an avid saver. He wants to put an equal amount each year from age 21 to 50 (30 years) such that starting at age 65 he can make a guaranteed annual withdrawal of $45,000 forever without touching the corpus, which will be the inheritance money for his family. He will make no deposits during the years of age 51 through 65. At a conservative return of 6.5% per year for all the years, what amount must he invest each year from age 21 through 50?

The amount that must be invested each year is $

Expert Solution

He will be making annual withdrawal of $45,000 starting the year 65 years for an infinite time period. Thus the amount will be equal to the interest income of the deposit. Assume the corpus amount is $A and interest income = $45,000

A = 45,000/0.065 = $692,307.69

Corpus amount = $692,307.69

Now assume the annual deposit made by the investor = $S

S = 629,307.69 (A/F, 6.5%, 30) (P/F, 6.5%, 14)

S = 629,307.69 * 0.0116 * 0.4141

S = $3,325.5415

Rahul Sunny answered 2 years ago

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