1. QR Workshop – Finance November 5, 2015 ANDREAS KAKOLYRIS-YOONHEE KANG QUANTITATIVE REASONING FELLOW, NYCCT

2. Learning Objectives 1)Simple Interest 2)Compound Interest Rate 3)Annuity

3. Simple Interest Simple interest is a one-time percent of an amount of money. With simple interest, you pay/earn the same amount of interest every year. You invest $1,000 at 20 % simple interest! Interest = 1000(0.2)=200 Value in one year = 1,000 (initial invest) + 200 (interest)= $1200 Value in two years = 1,000+ 400 (interest for 2 years) = $1,400 $1,000 1,200 1400 1,600 Today 12 3 4 1,800 …

4. Simple Interest I = Prt Future Value (FV) = P + I = P(1+rt) I = interest P = the beginning amount borrowed or invested ("Principal") r = interest rate t = time; the length of the time loaned or invested FV (A)= the final amount repaid or accumulated

5. Compound Interest Compound interest is a percent of an original amount, as well as a percentage of the new amount including previously calculated interest. With compounding we work out the interest for the first period, add it the total, and then calculate the interest for the next period.  interest on interest!

6. Compound Interest Rate $1,000 1,200 1,440 1,728 Today 12 3 4 2,073.6

7. Compound Interest Rate FV = PV(1 + r) t

8. Compound Interest Rate **Interest can be compounded annually (once a year)  n=1 semiannually (twice a year)  n=2 quaterly (4 times a year)  n=4 monthly (12 times a year) daily (365 times a year)

9. Simple VS Compound Year 20% Simple Interest20% of Compound Interest PrincipalInterestPrincipalInterest 0 (Today)1000 1 2001200200 210002001440240 310002001728288 410002002073.6345.6 Value after 4 yr 18002073.6

10. Compound Interest Rate

12. Compound Interest Rate_Example1 Find the FV of $800 after 5 years with APR=12% with monthly compounding Today 12345 FV 800 Compounding

13. Compound Interest Rate Today 1234 FV PV Today 1234 FV PV Compounding Discounting we moved single cash flows forward and backward in time.