Interest Rates Annual Interest Rate Year Balance Now
Interest Rates
Annual Interest Rate Year Balance Now P 1 P + r. P 2 (P + r. P) + r(P + r. P)
Cleaned up Year Now 1 2 … N Balance P P(1 + r)2 … P(1 + r)n
Periodic Compounding O
Continuous Compounding O
Solving for this limit O
Recall for your Math Days O
So…. O
Continuous Rate of Change O Let f(t) = Petr O Taking the derivative, we get: f ’(t) = (Petr )’ = r Petr = rf(t) O In words: "at any instance, the balance is changing at a rate that equals r times the current balance"
Present/Future Value from Present value, time and rate FV = PV(1 + r)n Present Value from Future value, time and rate PV = FV/(1 + r)n Rate from Present, Future value and time r = (FV/PV)1/n - 1
Ex) Investment choice Investment A Investment B PV $1000 FV $3000 $4000 n 5 7 r 24. 57% 21. 90%
Simple/Compound Interest O
Nominal vs. Effective Rates O
EAR vs. APR example O
Effective Rate (ER) vs. Nominal Rate (NR) O
Ex) Effective Interest Rate O
Cash flows O A stream of cash exchanges between 2 parties following a agreed upon schedule Example O Jim gives Mary $300 today O Mary gives Jim $500 a year from now O Jim gives Mary $200 two years from now. O From Jim’s point of view the cash flow is: [ -$300, $500, -200] Note: cash flow agreements where the sign(+/-) of the amounts start negative and at a point switch to positive and stay positive is referred to has an Investment
IRR – Internal Rate of Return Example 1 : Consider the cash flow below: O You pay $100 today O You receive $105, one year from today. Note: this is an investment What is the interest rate of this cash flow? O Present Value: -$100 + $105/(1+r) = 0 O Future Value: -$100(1+r) + $105 = 0
IRR – Internal Rate of Return O
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