EC2509691 sSU18 Help Save Exit Submit How much must you dep

EC250-9691 s-SU18 Help Save & Exit Submit How much must you deposit each year into your retirement account starting now and continuing through year to withdraw $100,000 per year forever, beginning 28 years from now? Assume the account e 9 if you want to be able arns interest at 13% per year. The amount to be deposited is determined to be $ K Prev 10 of 10 Next> m now ? Assume the account earns interest at 10% per year. The amount to be deposited is 0

Solution

ANSWER:

We will 1st find out the present value of amount of $100,000 per year till perpetuity at i = 13%

pv = amount(p/a,i,n)

pv = 100,000(p/a,13%,infinity)

pv = 100,000 * 7.692 = $769,200

so at the end of the 28th year he will need $769,200 which is the future value of the amount that he needs.

now we will find the present value at year 0 with i = 13%

pv = fv(p/f,i,n)

pv = 769,200(p/f,13%,28)

pv = 769,200 * 0.0326 = $25,075.92

now we will find out the amount that needs to be deposited for 9 years.

amount = pv(a/p,i,n)

amount = 25,075.92(a/p,13%,9)

a = 25,075.92 * 0.1949 = $4,887.29

so the amount that he needs to deposit is $4,887.29 for 9 years.