Question

A couple will retire in 50 years; they plan to spend about $32,000 a year in retirement, which should last about 25 years. They believe that they can earn 9% interest on retirement savings.

a. If they make annual payments into a savings plan, how much will they need to save each year? Assume the first payment comes in 1 year. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. How would the answer to part (a) change if the couple also realize that in 20 years they will need to spend $62,000 on their child’s college education? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Annual wothdrawal=$32000

No of withdrawal=25

r=9%

PV of withdrawal =A*(1-(1+r)^-n)/r

=32000*(1-(1+9%)^-25)/9%

=32000*(1-1.09^-25)/0.09

=32000*(1-0.116)/0.09

=32000*0.884/0.09

=$314322.55

Answer a

FV of deposits= PV of withdrawal

No of deposits=50

FV= A*((1+r)^n-1)/r

Or, 314322.55=A*((1+9%)^50-1)/9%

Or, 314322.55=A*(1.09^50-1)/0.09

Or, 314322.55=A*(74.3575-1)/0.09

Or, 314322.55=A*73.3575/0.09

Or, A=314322.55*0.09/73.3575

Or,A=$385.63

Each year saving must be $385.63

Answer b

For FV of $62000 at 50th year , n=50-20=30

FV=62000*(1+9%)^30=62000*1.09^30=62000*13.2677=$822596.07

Total FV =314322.55+822596.07=$1136918.62

FV= A*((1+r)^n-1)/r

Or, 1136918.62=A*((1+9%)^50-1)/9%

Or, 1136918.62=A*(1.09^50-1)/0.09

Or, 1136918.62=A*(74.3575-1)/0.09

Or, 1136918.62=A*73.3575/0.09

Or, A=1136918.62*0.09/73.3575

Or,A=$1394.85

Hence annual deposit will be $1394.85