Lecture 5: Interests & Annuities

Question 1

Simple Interest Equation

Answer 1

Simple Interest = P x r x t
P - principal
r - interest rate
t - time in years

Question 2

Principal

Answer 2

The amount being borrowed

Question 3

Maturity date

Answer 3

The specific date on which the principal amount of the debt is due- along with interest

Question 4

Interest Rate

Answer 4

Often published as % APR (annual percentage rate) which is normally prorated to daily/monthly rate

Question 5

Fixed Interest Rate

Answer 5

Does not change overtime, therefore can be calculated using a simple interest formula 

Question 6

Overnight policy rate (OPR)

Answer 6

Set by bank of Canada for banks to lend money to each other at the end of the day (to balance all transactions, i.e. money transferred in vs. money transferred out)

Question 7

Bank Rate

Answer 7

Set by bank of Canada for financial institution to borrow overnight (one day loan) from the central bank

Question 8

Prime Rate

Answer 8

Set by financial institutions, based on bank of Canada’s policy rate, which is been passed down to borrowers
(It is the lowest rate of interest at which money may be borrowed commercially)

Question 9

Variable Interest Rate

Answer 9

Can change over time – usually using the prime rate as a benchmark
(Interest rate on a loan or security that fluctuates over time)

Question 10

Actual Variable Rate

Answer 10

Offered to borrowers and typically includes a plus/minus percentage spread, depending on the borrower’s credit worthiness

Question 11

Price of a Loan (4 Factors)

Answer 11

POLICY RATE (same as OPR) - set by central bank(to lend money to each other at the end of the day (to balance all transactions, ie money transferred in vs. out)
BANK RATE: set by Bank of Canada for financial institutions who wish to borrow overnight (one day loan) from the central bank
PRIME RATE: set by financial institutions based on Bank of Canada’s policy rate, which is then passed on to borrowers (the lowest rate of interest at which money may be borrowed commercially)
VARIABLE RATE: +/- percentage spread based on credit score

Question 12

Fixed Income Interest

Answer 12

Provides a fixed rate of return for a set timeframe. Is generally low & payable at set intervals (I.e. monthly, quarterly or annually)

Question 13

Common types of Fixed Income Products

Answer 13

GIC- Guaranteed Investment Certificates (sold by Canadian banks and trust companies. Insured up to 100k. Minimum term is usually 12 months. Principal returned to the lender at maturity date.)
Savings Account- (Interest bearing deposit account held at a bank or other financial institutions. Safe & pays a moderate interest rate.)
Bonds- (Short term debt backed by Canadian Gov’nt. Min. purchase is $5k, in $1k denominations. Some larger corps also issue bonds. Interests b’tween 1.4%-3.5%

Question 14

Compound Interest

Answer 14

Earning interest on both the principal & accumulated interest, which can result in significant growth over time
- Requires that principal & accumulated interest must be reinvested over Time based concepts of time value of money

Question 15

Compound Interest Calculation

Answer 15

A = P(1 + r/n) nt (exponent)
A - accumulated amount
P - Principal
r - interest rate
t - time in years
n - number of times interest is compounded in a year

Question 16

Annuity

Answer 16

A series of payments, usually of equal size, made at periodic time intervals.
(E.g. personal: contributions to RRSP, RESP, student loans, car loans, Business: equipment loans, mortgages, lease contracts)

Question 17

Constant Growth

Answer 17

Growth annuity where payment grows a fixed percentage with each subsequent payment

Question 18

Perpetuity

Answer 18

An annuity that has no end

Question 19

Annuity Present Value Formula

Answer 19

PV annuity = (Annuity/r) (1 - 1/(1+r) t (exponent)
PV- present value
Annuity- annuity payment period ($)
t - Number of periods
r - Yield to Maturity (YTM) [annual interest rate of return]

Question 20

PV of an Ordinary Annuity

Answer 20

PV of an ordinary Annuity = R * 1- (1 + i) -n (exponent)/i
i = interest rate per compounding period
n = The number of compounding periods
R = Fixed Periodic Payment