Meaning Of Interest Rates Flashcards
Future value (FV)
Future value of an investment made today
Future value formula
PV x (1+i)
Future value with compound interest formula
E.g 2 years at 5% interest
FV = PV x (1+i) to the n
For 2 years would be PV x (1+0.05)²
Present value definition
Value today of a payment to be made in the future
PV formula
PV = FV / (1+i) to the n
If a payment is to be made sooner than later, is the present value worth more or less
Worth more
I.e an increase in time reduces present value.
How does interest rates link with present value
Higher interest rate, lower present value.
Bond definition
Promise to make a series of payments on specific future dates
2 terms of bonds
Requires the borrowers to make payments to lender.
Specify what happens if failure to do so.
The price of bonds depends on the characteristics:
What are the types?
Zero-coupon bonds/discount bonds
Fixed payment loans
Coupon bonds
Consol or perpetuity
Zero coupon/discount bonds
A single future payment. Price is less than face value (hence why called discount).
What is the price of zero coupon bonds
The price is just the present value of the payment on the future date.
Price of a zero coupon bond for a year, and 6 month
It is just present value of the payment to be made at the future date as mentioned before
Face value/(1+i)
For 6 months:
Face value/(1+i)¹/²
- Fixed payment loans, formula and provide example
Sum of present value of the payments.
E.g home mortgages, car loans
Fixed payment/(1+i) + Fixed payment/(1+i)² + … + Fixed payment/(1+i) to the n
- Coupon bonds, definition and formula
Issuer of bond promises to make a series of periodic interest payments, plus a principal payment at maturity (the end).
Coupon payment/(1+i) + Coupon payment/(1+i)² + … + Coupon payment/(1+i) to the n + Face value/(1+i) to the n
Last bit is the principal payment at maturity.
- Consol or perpetuity, definition and formula
Issuer promiser to make a series of periodic interest payments FOREVER.
Yearly coupon payment / i
Nominal yield
Stated rate of bond.
Yield to maturity
The yield received if they hold the bond till its maturity (when final principal payment is made)
(The best to measure the return of holding a bond)
Current yield definition and formula
The interest rate of the bond given its current price.
Current yield = Yearly coupon payment/Price paid
(I.e the return from solely the coupon payments)
Price yield relationship and diagram pg 20
Why?
Inverse relationship.
Why? As price is the present value of cash flows. (PV formula)
3 types of bond
Par
Discount
Premium
Par bond
Bond price = face value
Coupon rate = current yield = yield to maturity.
Discount bond
Bond price<Face value (as mentioned earlier)
Coupon rate < Current yield < Yield to maturity
Premium bond
Bond price > face value
Coupon rate > Current yield > Yield to maturity
Holding period return
Return of holding a bond and selling before maturity.
Whenever bond price changes, there is a capital gain/loss
What happens to holding period return following a fall in the price at which a bond is sold
Decrease, since lowers capital gain
