This is a classic retirement problem. A time line will help in solving it. Your

Question

This is a classic retirement problem. A time line will help in solving it. Your friend is celebrating her 35th birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw $134,000 from her savings account on each birthday for 20 years following her retirement; the first withdrawal will be on her 66th birthday. Your friend intends to invest her money in the local credit union, which offers 7.9 percent interest per year. She wants to make equal annual payments on each birthday into the account established at the credit union for her retirement fund.

If she starts making these deposits on her 36th birthday and continues to make deposits until she is 65 (the last deposit will be on her 65th birthday), what amount must she deposit annually to be able to make the desired withdrawals at retirement? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make one lump sum payment on her 35th birthday to cover her retirement needs. What amount does she have to deposit? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Suppose your friend

This is a classic retirement problem. A time line will help in solving it. Your friend is celebrating her 35th birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw $134,000 from her savings account on each birthday for 20 years following her retirement; the first withdrawal will be on her 66th birthday. Your friend intends to invest her money in the local credit union, which offers 7.9 percent interest per year. She wants to make equal annual payments on each birthday into the account established at the credit union for her retirement fund.

Explanation / Answer

a.If she starts making these deposits on her 36th birthday and continues to make deposits until she is 65 (the last deposit will be on her 65th birthday), what amount must she deposit annually to be able to make the desired withdrawals at retirement? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

She will withdraw PMT = 134000 every year for nper = 20Yrs & then corpus = FV = 0.

So She needs at Y65, a corpus =PV(rate,nper,pmt,fv)

= PV(7.9%,20,-134000,0)

= $1,325,480.14

Now at agr of 35,

So No of payments = nper = 65-35 = 30

Rate = 7.9%

Corpus at Age of 65 = FV = $1,325,480.14

Initial value of corpus = PV=0

So Annual Deposit reqd to get $1,325,480.14 at age of 65 = PMT(rate,nper,pv,fv)

= PMT(7.9%,30,0,1325480.14)

= $11,916.99

Annual deposit amount = $11,916.99

b.Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make one lump sum payment on her 35th birthday to cover her retirement needs. What amount does she have to deposit? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Here we have FV = $1,325,480.14, i=7.9%, n=30

So AMount of deposit = PV = FV/(1+i)^n = 1,325,480.14/(1+7.9%)^30

Amount deposit $135,434.68

c.Suppose your friend

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