In: Finance
You have been saving $100/month for the last 10 years in a retirement account that earns 1% interest monthly.
(a) How much money do you have in your retirement account today? (25 points)
(b) If you STOP making contributions to your retirement account, but leave the amount you currently have in it to continue earning interest at 1% per month, how much money will you have in your retirement account when you retire in 30 years? (20 points)
(c) You expect to live another 25 years after you retire. Your plan is to make equal monthly withdrawals from your retirement account over this 25-year retirement period such that the account is fully exhausted. How much money can you withdraw each month? Assume that you continue to earn 1% per month on your retirement savings. (20 points)
Answer (a):
Monthly savings = $100
Monthly interest = 1%
Number of months = 10 * 12 = 120 months
For ordinary annuity:
FV = Periodic annuity * ((1 - Periodic Interest rate) Number of periods - 1)1/ Periodic Interest rate
= 100 * ((1 + 1%) 120 - 1) /1%
= $23,003.8689
Amount in your retirement account today = $23,003.87
Answer (b):
Number of months = 30 * 12 = 360
FV = PV * (1 + Periodic interest rate) Number of periods
= 23003.8689 * (1 + 1%) 360
= $826980.84
Money you will have in your retirement account when you retire in 30 years = $826,980.84
Answer (c)
Number of months (retirement period) = 25 * 12 = 300
The question does not tell whether withdrawal is done at beginning of month or at the end of month.
Hence two answers are given.
(i) In case withdrawal is done at the beginning of month:
Money you can withdraw per month = PMT(rate, nper, pv, fv, type)
= PMT(1%, 300, -826980.84,0,1)
= $8,623.72
Money you can withdraw per month if drawn at beginning of month = $8,623.72
(ii) In case withdrawal is done at the end of each month:
Money you can withdraw per month = PMT(rate, nper, pv, fv, type)
= PMT(1%, 300, -826980.84,0,0)
= $8,709.96
Money you can withdraw per month if drawn at the end of month = $8,709.96