Time Value of Money

Question 1

What is an interest rate?

Answer 1

proportion of loan charged as interest, expressed as a percentage

Question 2

What is a real risk-free rate?

Answer 2

theoretical rate on a loan when inflation is not considered

Question 3

What is a nominal risk-free rate?

Answer 3

rate on loan with inflation considered

Question 4

Name 3 main risks of securities

Answer 4

Default risk, liquidity risk, maturity risk

Question 5

What is required rate of return?

Answer 5

return that compensates for inflation and associated risks

Question 6

Formula for required rate of return

Answer 6

RRR = real risk free rate + inflation premium + default risk premium + liquidity premium + maturity risk premium

Question 7

EAR - effective annual rate formula

Answer 7

EAR = (1 + r/m)^m - 1

Question 8

Future Value Formula (compounding)

Answer 8

FV = PV(1 + r/m)^nm
FV = PV*exp(rn)

where m = number of compounding periods in a year
n = number years

Question 9

Present Value Formula (discounting)

Answer 9

PV = FV/((1+r/m)^nm)
PV = FV*exp(-rn)

where m = number of compounding periods in a year
n = number years

Question 10

What is an annuity?

Answer 10

series of equal cash flows; evenly spaced; finite number of cash flows

ordinary: end of period
due: beginning of period

Question 11

What is a perpetuity?

Answer 11

series of equal cash flows; evenly spaced; infinite number of cash flows

Question 12

Future value of annuity formula

Answer 12

ordinary
FV = A [((1+r)^n - 1) / r ]

due
FV = A [((1+r)^n - 1) / r ][1+r]

where A = amount received for period

Question 13

Present value of perpetuity formula

Answer 13

PV = A / r

Question 14

Present value of annuity formula

Answer 14

ordinary
PV = A [(1 - (1+r)^(-n)) / r ]
PV = A [(1 - (1+r/m)^(-nm)) / (r/m) ]
due
PV = A [(1 - (1+r)^(-n-1)) / r ] + A
PV = A [(1 - (1+r/m)^(-n-1)(m)) / (r/) ] + A
where A = amount received for period

Question 15

Growth rate formula

Answer 15

g = (FV/PV)^(1/N) - 1