Chaper 6 in-class problem.
Solution: We are dealing with two annuities and want to make them equal. To do this, I will make the FV of the first equal to the PV of the second as of the day I retire. Another way to say this is that I want to have just enough money when I retire to fund my retirement (assuming that I live 20 years post retirement) with nothing left over for my relatives. Problem is not specific about compounding periods—assume annual and use a prorate or straightline approach for subperiods like 6 months (e.g., 6 months interest = ½ annual interest).
Make a timeline!!
Assume the S = amount saved each year.
End of year y
1 2 3 4 5 6 7 8 9 10
10 11 12………………………….29 30
at the end of year 10, FV1A = 12.5779 * S
at the middle of year 11, PVAD = 14.13394 * $72,000 = $1,017,643.60
Now solve for S: 12.5779 S = $1,017,643.60 / (1 + .02)
S = $79,320.856
(12.5779 S)*(1 + .02) = $1,017,643.60
12.829458 S = $1,017,643.60
S = $79,320.856 (ouch!)
APR (annual percentage rate) = periodic rate*number of periods/yr. E.g., 1% monthly return = 12% APR
APY (annual percentage yield) = effective or true rate, takes into account compounding. E.g., 1% / month = 12.68% APY [((1.01)^12) – 1].
ARR (annual rate of return) can be calculated different ways and therefore, could be either APR or APY or something else.
Credit card companies advertise 18% APR, this equals 1.5%/month which equals 19.56% APY.
Interperiod interest is prorated (e.g., 4% APR compounded annually means that 6 month rate is .04/2 = 2%.) If annual compounding (rare these days), then APR = APY!
How to calculate an APR interest rate? Upgrade to Pro Divide your finance charges by the total balance, then multiply by 1200 to get your APR. ... Find the current balance on your card using the most recent statement. ... Find the finance charge on your card using the most recent statement. ... Divide your finance charge by the amount owed. ... Multiply the answer by 100 to get a percent. ... More items...