Question

In: Finance

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

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

The value of the perpetuity as of age 65

V₆₅ = CF/r * (1 + r)

V₆₅ = 45,000/0.065 * (1 + 0.065)

V₆₅ = $737,307.6923076923

Now, we will discount this by 15 years to get the value as of age 50

V₅₀ = V₆₅/(1 + r)^n

n = 65 - 50 = 15

V₅₀ = 737,307.6923076923/(1 + 0.065)^15

V₅₀ = $286,684.7874445102

Finally, with this as the future value let's find the annual payment required for 30 years

FV₅₀ = 286,684.7874445102

The amount that must be invested each year is $3,319.0765694423

jeff jeffy answered 2 years ago

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