Quantitative Methods and Economics: Reading 1 - Time value of money

Question 1

Explain concept of compound interest

Answer 1

growth in the value of the investment from period to period reflects not only the interest earned on the original principal amount but also on the interest earned on the previous period’s interest earnings - interest on interest

Question 2

What are the 3 way (words) that can be used to define

Answer 2

• Required rate of return
• Discount rate
• Opportunity cost

Question 3

Interpret interest rates as required rates of return, discount rates, or opportunity costs.

Answer 3

Required rate of return : Return that investors and savers require to get them to willingly lend their funds

Discount rate: If individual borrows at an interest rate of 10%, then that individual should discount payments to be made in the future at that rate in order to get their equivalent value in current dollars or other currencies

Opportunity cost: If the market rate of interest on 1 year securities is 5%, earning an additional 5% is the opportunity forgone when current consumption is chosen rather than saving

Question 4

Explain an interest rate as the sum of a real risk-free rate and premiums that compensate investors for bearing distinct types of risk.

Answer 4

Real risk-free rate of interest is a theoretical rate on a single-period loan that has no
expectation of inflation on it.

Example: US treasury bill (T-bill) are nominal risk-free rates because they contain an inflation premium.
nominal risk-free rate = real risk-free rate + expected inflation rate

Real rate of return, we are referring to an investor’s increase in purchasing power (after adjusting for inflation)

Lots of different premiums that compensate for:
- Inflation premiums
- Default risk premiums
- Liquidity premium
-Maturity risk premium

Question 5

What is a default risk?

Answer 5

The risk that a borrower will not make the promised payments in a timely
manner.

Question 6

What is a liquidity risk

Answer 6

The risk of receiving less than fair value for an investment if it must be sold for
cash quickly.

Question 7

What is a maturity risk

Answer 7

As we will cover in detail in the section on debt securities, the prices of longer-term bonds are more volatile than those of shorter-term bonds. Longer maturity bonds have more maturity risk than shorter-term bonds and require a maturity risk premium.

Question 8

Calculate the FV of a single sum and say the equation in variables:

Calculate the FV of a $200 investment at the end of two years if it earns an annually compounded rate of return of 10%.

Answer 8

FV = PV (1+I/Y)**N

$242

Question 9

Calculate the FV of a single sum and say the equation in variables:

Given a discount rate of 10%, calculate the PV of a $200 cash

Answer 9

FV/((1+I/Y)**N)

-165.29

Question 10

What is an annuity?
And what are the 2 types of annuities?

What is the future value of an ordinary annuity that pays $200 per year at the end of each of the next three years, given the investment is expected to earn a 10% rate of return?

Answer 10

Equal stream cash flows at equal intervals over a given period.

1. Ordinary annuities: cashflow occur at the end of each compounding period
2. Annuities due: Payments at beginning of period

Question 11

: PV of an ordinary annuity beginning later than t = 1

What is the present value of four $100 end-of-year payments if the first payment is to be received three years from today and the appropriate rate of return is 9%

Answer 11

2 step! find the PV at t=3 : 323.97
then solve PV t=0 : 272.68

Question 12

Holding period return

Answer 12

end-of-period value/beg of period value -1