Chapter 5 - The Principles Of The Time Value Of Money

Question 1

Compound Interest Formulas - formula and work out

2000 and 5% for five years

1000 and 3% for four years

Answer 1

FV = PV (1+interest rate)n

2000*(1+0.05)5(squared) = 2552.56

1000*(1+0.03)4 = 1125.31

Question 2

How to work out compound rate of return - example (see card)

PV = 10,000
FV = 15,785
5 Years

And how calc’d if interest rate changes

Answer 2

1. 5785 under the bridge thing
2. 0956-1 = 0.0956 x 100 = %

If interest rate changes then do usual calc but split into two i.e. (1+%)2*(1+%)3

Question 3

Interest payable at more frequent rates - how to work out annual, biannual and quarterly interest accrued

EAR formula + example;
8% and quarterly

Answer 3

Annual interest - PV1.10
Biannual interest - PV1.05(2)
Quarterly interest - PV*1.025(4)

EAR = 1+%/years(years)little-1
E.g. = (1+0.08/4)4-1
= (1.02)4-1
= 1.0824-1 = 8.24%

Question 4

APR or AER formula (EAR)
- what are each used for

Present value - formula
Eg 1000, 5% & 5 years

Answer 4

APR used as loans rather than deposits (AER)

Worked out same way as EAR

PV = FV/(1+%)years(little)
= 783.53

Question 5

Accumulation of regular savings

Answer 5

Can calculate regular payments accrued interest year by year at end of term. Formula;
FV= P (1+%)year-1/%
P= regular payments

E.g
100*(1+0.08)10-1/0.08
FV = £1,448.66

Question 6

Discounting of regular savings - what are compounding and discounting (calcing what)

Discounting - used to arrive at what

• compare PV and actual value to work out what
• dividends and affect on PV after discounting

Discounted formula

Answer 6

Compounding - calculating future value
Discounting - calculating present value of an investment
- used to arrive at a fair value of investment price
- can then compare PV against actual current value and work out if its under or overvalued and therefore worth buying or selling.
- when paying dividends, present values after discounting may be uncertain.

Discounted cash flow formula;
PV = FV/(1+%)years

Question 7

Real returns & nominal returns

Real return formula (simple) & eg 11% return and 3% inflation

Nominal - used to work out what and formula (simple)

Answer 7

Real = nominal return - inflation rate

E.g. 11% return, 3% inflation
11%-3% = real rate of return

Nominal = real +inflation (works out expected returns)
E.g. inflation expected to be 2.5% and wants to achieve 4% so therefore needs to generate 6.5%.

Question 8

Calculating sum of money needed to provide regular payments (annuity)

Annually and monthly + how to work out regular needed to reach nil balance

Eg 1 - annual - 100£, 10 years and 8%
Eg 2 - monthly nil balance - £30,000 A, 3% & 6 yearso

Answer 8

A = reg payment*(1-(1+%)-y/%)
As above with months instead.

If needed to work out how much to draw to reach nil balance, divide A but () to find P

Eg 1 = 671.01
Eg2 = 455.81