Time Value of Money

Question 1

What are EAR’s, APR’s and effective rates for holding periods?

Answer 1

• e.g. bank offers you a loan at 6% pa w/ monthly compounding
• > effective rate is 0.5%

Question 2

How does time value of money work?

Answer 2

• e.g. 300 grows to 320 in 6months, what is the annual interest rate?
• > 320/300 = rate for 6months, square for 1year

Question 3

Perpetuity

Answer 3

• on formula sheet
• goes forever

perp. due
- > (1+r) x PMT/r

perp. deferred
- > 1/(1+r)^k * PMT/r

Question 4

annuity

Answer 4

• on formula sheet

= annuity due
-> PMT/r * (1-1/(1+r)^n-1) + PMT

= deferred annuity
-> first payment beyond first period

-> 1/(1+r)^k-1 * (PMT/r) * (1-1/(1+r)^n)

Question 5

Amortisation

Answer 5

• Work out payment for annuity and then subtract equal payment from every year
• Remember to subtract interest from pmt amount
• Then subtract this new number (pmt-interest) from opening balance
• then work out new interest
  (opening balance - new number) * rate

Question 6

converting interest rates

Answer 6

coc -> discount rate

(1+coc)^1/n -1

converting interest rates
(1+r12months)^12 = 1+ryear

EAR(real interest rate) = (1+APR(nominal)/number of compounding periods)^M -1

Question 7

Inflation

Answer 7

(1+Rnom)=(1+Rreal)(1+Rinflation)