1. Fintech Chapter 7: Time Value of Money: Interest, Bonds, Money Market Funds

2. Importance of credit markets
Resources to borrowers
Income to lenders
Consumer preference to use resources now. Need to be compensated to defer

3. Future Value
$1000 today Interest rate r = 5% Future Value: principal plus interest = $1,000 + ($1,000 x0.05) = $1050 Future Value = Present Value plus interest Year two = $1,000 + ($1,000 x0.05) + (($1,000 x0.05) x 0.05)

4. Future Value = Present Value plus interest
Year two
= $1,000 + ($1,000 x0.05) + (($1,000 x0.05) x 0.05)
Compounding of interest
Future Value = Present Value plus interest
Future Value = Present Value x (1+r)n

5. Future Value = Present Value plus interest
Interest in Year Two on the Interest earned in Year One, or
$ $1000 x $1000 x (($1000 x 0.05) x 0.05), or
FV = PV + (PV x r) + (PV x r) + ((PV x r) x r)) .
With some modest manipulation, we get:
FV = PV x (1+ r + r +r2)
= PV x (1 + 2r + r2)
And noting that (1 + 2r + r2) = (1 + r)2,
FV = PV x (1 + r)2.
$1000 x (1.05)2.
More generally,
FV = PV x (1 + r)n
Where: r = interest rate and
n = the number of periods.

6. Use financial calculator to determine FV
Rule of 72: divide 72 by whole number to get approximation ( 7% doubles in 10 years)

7. Present Value Future Value = Present Value x (1+r)n
Present Value= Future Value /(1+r)n
Use PV to compare alternative investments
Additive property allows summing of individual PVs of different payments

8. Credit Instruments Simple Loan Fixed Payment Loan Coupon Bond
Zero-Coupon Bond

9. Yield to Maturity Need to compare returns from alternative investments
P=PV= (CF1 / (1+r)1) + (CF2 / (1+r)2 ) + … + (CFn / (1+r)n )
Where P = price of the instrument
PV= Present Value
CFn = Cash Flow from the instrument in period n
r = interest rate which also equals the Yield to Maturity.

10. Fisher’s Law The nominal rate equals the real rate plus inflation
i= r+ p
Where i= the nominal rate of interest
r= the real rate
p=the expected rate of inflation

11. Term Structure and Yield Curve
Positive= upward sloping
Flat=constant yield
Negative= downward sloping
Operation twist

12. Term Structure and Yield Curve

13. Moody’s Seasoned Aaa Corporate Bond Yield

14. Bond Yields for a Variety of Issues and Maturities

15. Factors Impacting Bond Prices
Wealth
Expected return
Risk
Liquidity
Tax treatment

16. Types of Debt Instruments
unsecured loans between banks
repurchase agreements (“repos”)
commercial paper
large denomination negotiable certificates of deposit
banker’s acceptances
funding agreements
money market funds

17. Fintech Applications Bond trading platforms Bond issuance
Information and analytics