Question

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% per year for all the years, what amount must he invest each year from age 21 through 50

Answer 1

$3,958.47

Step-by-step explanation:

we must determine the present value of his savings at age 65:

present value = annual withdrawal / 6% = $750,000

the present value of his savings at age 50 = $750,000 / (1 + 6%)¹⁵ = $312,949

annual contributions = $312,949 / 79.058 (FVIFA, 6%, 30 peridots) = $3,958.47