You and your financial advisor have been working on your retirement plan. You te
ID: 2819100 • Letter: Y
Question
You and your financial advisor have been working on your retirement plan. You tell him that your top fear is outliving your money. You decide that you’ll need $50,000 per year in perpetuity once you retire at age 65. Ignoring inflation, if you can earn a 5% return per year, how much money will you need in your retirement account at 65?
Assume you’re currently 40 with nothing saved for retirement. If you can earn an annual return on your investments of 10%, what should be your monthly contribution to your retirement account?
If you immediately inherited $50,000 and put it toward your retirement account, what is your new monthly contribution to your retirement account?
Your financial advisor tells you that 10% is a fairly aggressive goal for a retirement account at your age. You tell him that you can probably contribute $700 per month. What APR will your retirement account need to return to hit your retirement goal?
Explanation / Answer
1.
Present value of perpetuity = Cashflow/Interest rate
= 50000/0.05 = $1000000
2.
You have 25 years to save for your retirment, which required $1000000
Future value of annuity is given by,
FV of annuity = P*[((1+r)^n - 1)/r]
P - Periodic payment = ?
r - rate per period = 0.1
n - number of periods = 25
1000000 = P*(((1+0.1)^25 - 1)/0.1)
P = $10168.07
If you receive $50000, It's worth in 25 years will be
FV = PV*(1+r)^n = 50000*(1+0.1)^25 = $541735.30
Additional amount required = 1000000-541735.30 = $458264.70
FV of annuity = P*[((1+r)^n - 1)/r]
458264.70 = P*(((1+0.1)^25)-1)/0.1)
P = $4659.67
3.
FV of annuity = P*[((1+r)^n - 1)/r]
1000000 = 700*(((1+r)^25)-1)/r)
r = 0.8693%
APR = 0.8693%*12 = 0.1043 = 10.43%