Warm-up: Compound vs. Annuity! 1) How much will you have after 5 years if you deposit $500 twice a year into an account yielding 3% compounded semiannually? 2) How much money is in the bank after 3 years if you deposit $100 earning 2% compounded quarterly? 3) What is the monthly payment if you want to save $25000 in 10 years, if the bank will give you 1% compounded monthly?
Mon. April 23 rd Warm-up Go over HW/? s Notes: Present Value/Amortization Start HW
Annuities continued It s all about PERIODIC payments You put in the same amount each month/quarter/year, / and the bank applies interest (compounds) to the amount in the account each month/quarter/year. S/R are the same equation!!! If you need to find out the future value, plug in all variables to the S equation. If you know the amount you need in the future and want to calculate the payments, use the R version of the equation. Notice, the equations are all +n Now, fast forward to the future
Annuities continued You ve been diligently saving your money for the last 10/20/30 years, and now it s time to spend it! Wohooo!!!! If it s your college fund, are your folks going to give you the lump sum and walk away, so you can buy a new car/splurge? If you are ready to retire, do you cash out and take the lump sum and hide it under your mattress? The correct answer to the questions is NO! You will be taking out periodic payments!!! ( -n n ) What was once the future value (S) is the Present Value (P) because, remember we fast-forwarded to the future
Present Value of an Annuity Beware: The formula looks similar il to future value!! Variables are moved around, but mainly notice -n means that you are not adding money, rather taking it out over time! P = R = Periodic Payment ( ) n = R[1 1+ i ] P = Present value of all payments i = rate per period (i = r/m) i n = number of payments (total periods) EX) What is the present value of an annuity that pays $500 per month for 4 years if the interest rate is 3% compounded monthly? (cashing out a College fund!!!) This is not the example on your paper just tune in!!!
Present Value of an Annuity You try do the example on the front of the worksheet (change it a little first: $2000 & 15 years) see see if you get the right answer! P = R = Periodic Payment ( ) n = R[1 1+ i ] P = Present value of all payments i = rate per period (i = r/m) i n = number of payments (total periods) EX) What is the present value of an annuity that pays EX) What is the present value of an annuity that pays $2000 per month for 15 years if the interest rate is 6% compounded monthly? (Cashing out an IRA- retirement fund)
Amortization When you borrow (loan) money, solve the P formula for R, to find out what your payments are! Still n because you are paying off the loan! It s called the Amortization Formula: R = Pi [1 i n ( 1 + i ) ] R = Periodic Payment P = Present value of all payments i = rate per period (i = r/m) n = number of payments (total periods) EX) Assume that you buy a TV for $800 and agree to pay for it in 18 equal monthly payments at 1.5% interest per month on the unpaid balance. What are your payments & how much interest will you pay?
Wrapping it all up Once you are done saving, time has passed (you future value becomes the present value) and you are ready to take out the money over time this thi allows you to still earn interest on the sum, so it is still earning money, which makes it last longer! If you borrow money, you are paying it back over time also the process of figuring in out what you owe as time goes on is called amortization HW #37: Blue Worksheet do #1-9 for next class!
EX) You borrow $500 that you agree to repay in 6 equal payments at 1% interest per month on the unpaid balance. R = Pi a) Find the monthly payment. n [1 1+ i ( ) ] b) How much total interest did you pay? c) Create an Amortization schedule for your payments. # Payment Interest Unpaid Balance Reduction 0 1 2 3 4 5 6 Unpaid Balance
EX) You borrow $1,000,000 at 6% APR compounded monthly to buy a house and agree to pay it off in 30 yrs R = Pi a) Find the monthly payment. [1 1 + i n a) Find the monthly payment ( ) ] b) How much total interest did you pay? c) Create an Amortization schedule for the first 3 payments. # Payment Interest (monthly!) Unpaid Balance Reduction (payment minus interest) 0 1 2 3 d) After 25 years, how much of your loan is left to pay? Unpaid Balance