Question

You want to be able to withdraw $35,000 from your account each year for 20 years after you retire. If you expect to retire in 15 years and your account earns 5.8% interest while saving for retirement and 4.7% interest while retired:
Round your answers to the nearest cent as needed.

a) How much will you need to have when you retire?
$

b) How much will you need to deposit each month until retirement to achieve your retirement goals?
$

c) How much did you deposit into you retirement account?
$

d) How much did you receive in payments during retirement?
$

e) How much of the money you received was interest

Answer 1

Person wants to withdraw $35000 each year for 20 years after retirement.
Interest rate on the time of retirement is 4.7%

a). Amount which will need to have into account on retirement. We have to calculate the present value of Total Withdrawls and it is assumed that withdrawls are made at the end of year, not beginning.
PV = P*[(1-(1/(1+r)^n))/r]
Here PV = Present Value , P= Annuity, r = interest rate and n = time period
PV = 35000*[(1-(1/(1+0.047)^20))/0.047]
= 35000 * [(1-(1/2.5057))/0.047]
= 35000 * 12.7853 = $ 447,486.11
This is the amount required to be in the account on retirement. This can also be calulated using Excel or calculator.

b). Now the amount of $447,486.11 is the future value of the investments made at 5.8% annually for 15 years till retirement.Formula for Future Value annuity is
FV= P*[((1+r)^n - 1)/r]
447486.11 = P*[((1+0.058)^15 - 1)/0.058]
447486.11 = P*[(2.3296-1)/0.058]
447486.11 = P* 22.9244
P = $19520 i.e Amount to be invested annually till retirement.

c). Amount deposited in retirement account. $19520 * 15 years = $292,800.

d). Amount receive in payments during retirement. $35000 * 20 years = $700000. This is the total amount receive during retirement and includes interest.

e). Money received of interest = $700000 - $447486 = $252514. Here figures are approxed for exact amounts.