This document contains information about calculating present and future values for annuities using different interest rates and cash flows over time. It includes examples of calculating future value, present value, and future/present value of ordinary and annuities due. It also shows how to solve for the interest rate, payment, or number of periods given the other variables for an annuity. An example problem solves for the interest rate of a 36 month computer lease with monthly payments of $78 and a present value of $1988.13.

1. NO Descripton Data Year Year year Year Year
1 Interest rate 0.05
2 Time 0 1 2 3 4 5
3 Cash Flow -100
4 Future value 105 110.25 115.76 121.55 127.63
NO Descripton Data Year Year year Year Year
1 Interest rate 0.05
2 Time 0 1 2 3 4 5
3 Cash Flow 0 0 0 0 0 127.63
4 Present Value 100
NO Descripton Data Year Year year
1 Interest rate 0.05
2 Time 0 1 2 3
3 Cash Flow 100 100 100
4 Future value 315.25
Future Value
Present Value
Future Value of Ordinary Annuities
PMT(1+i)^n-1
i
FVA
FV= PV(1+i)^nEquation
PV
FV
(1+i)^n

2. NO Descripton Data Year Year year
1 Interest rate 0.05
2 Time 0 1 2 3
3 Cash Flow 100 100 100
4 Future value 331.01
NO Descripton Data Year Year year
1 Interest rate 0.05
2 Time 0 1 2 3
3 Cash Flow 100 100 100
4 Present Value 272.32
NO Descripton Data Year Year year
1 Interest rate 0.05
2 Time 0 1 2 3
3 Cash Flow 100 100 100
4 Present Value 285.94
i
(1+i)
Present Value Ordinary Annunities
PVA PMT (1- 1/(1+i)^n
i
Present Value Annunities Due
PVA PMT (1- 1/(1+i)^n
Future Value of Annuities Due
FVA Due
PMT(1+i)^n-1
i
(1+i)

3. Sometime it is useful to calculate the interest rate, payment or number of periods for a given annuity.
DATA
PV 1988.13
PMT 78
N 36
i.rate ?
solution
.+ 0 0
= 2% per month
24% Per year
Answer= you would probably want to buy a computer rather than lease it.
Annuities : Sovling For Interest rate , Number of Periods or Payment
i
1988.13(1.i)^36 + (-78) (1+i)^36-1
As an alterative ,you can buy it for $ 1988.13. in ither case computer will be worth zero. You would like to interest
rate the manufacturer has built in to lease, if that rate is too high, you should buy the computer rather than lease it.
For Example , suposse you can lease a computer from its manufacturer for $78 per month. The lease run for 36
months, with payment due at the end of the month.
PV(1+i)^n + PMT( (1+i)^n-1
i
.+FV = 0

4. For Example , suposse you can lease a computer from its manufacturer for $78 per month. The lease run for 36 months, with
payment due at the end of the month.

5. The lease run for 36 months, with