Chapter 5-investment principles and risk

Question 1

A lump sum of £20,000 is invested at 3% a year for five years. How much will be accumulated in five years?

Answer 1

FV = PV(1 + r)^n

£20,000 x (1 + 0.03)^5

£23,185.48

Question 2

Interest payable monthly at nominal rate of 6% a year. What is the annual effective rate

Answer 2

EAR/APR/AER = (1 + r/n)^n - 1

(1 + 0.06/12)^12 - 1

= 6.17%

Question 3

Which of the following building societies offers the more favourable rate? Building society a pays 5.7% annual interest, compounded half yearly. Building society B pays 5.65% annual interest, compounded monthly

Answer 3

AER = (1+r/n)^n - 1

BS A = (1+0.057/2)^2 - 1

A = 5.78%

BS B = (1+0.0565/12)^12 - 1

B = 5.8%

Building Society B offers a marginally better rate

Question 4

What amount has to be invested to accumulate £10,000 at the end of three years at an annual interest rate of 2%?

Answer 4

FV = PV(1+r)^n

10,000 = PV(1+0.02)^3

PV = 10,000/1.0612

Question 5

If the nominal rate of return on their investment at 6% and inflation is 3%, what is the approximate real rate of return?

Answer 5

R real = Rnom - Rinf
= 6% - 3%
The approximate real rate of return is 3%

Question 6

Formula for compound interest

Answer 6

Present value(1+interest rate)^no years

Question 7

The formula for effective rate and how to then get the Annual percentage rate AKA Annual equivalent rate

Answer 7

(1 + interest rate/no years)^no years - 1

To get APR or AER you multiply effective rate by 100 as to depict it as a percentage to 2 decimal places

Question 8

Formula for present value

Answer 8

Future value / (1 + interest rate)^no years

Question 9

Formula for the future value of a series of payments plus interest (AKA an annuity), and how is it altered to find monthly withdrawals

Answer 9

P((1-(1+r)^-n)/r) = A

For monthly withdrawals

R/12 and don’t forget it’s a % so decimalise it

N x 12 because the periods increase

Then solve to find P

Question 10

Formula for real returns and nominal returns

Answer 10

Real return = nominal return - inflation

Question 11

Formula for the accumulation and discounting of regular savings

Answer 11

FV = P(((1+r)^n-1)/r)

Question 12

The formula for effective annual rate (EAR)

Answer 12

(1+r/n)^n -1

This is used when the interest payable is at different periods to annually, because the interest accumulated is effected by the regularity of the interest paid

E.g

Annual 1000 x 1.1 = 1100
Half yearly 1000 x 1.05 x 1.05 = 1102.5

Question 13

Appropriate uses of annual percentage rate (APR), annual equivalent rate (AER) and effective annual rate (EAR)

Answer 13

All of these have the same formula (1+r/n)^n - 1

EAR is used for loans and deposits
APR is used for loans
AER is used for deposits

Question 14

Sam has £30,000 invested in a building society paying a nominal rate of 3% per year interest is credited a monthly and he intends to draw out capital and interest monthly so that at the end of six years the account has a nil balance how much can Sam withdraw at the end of each month

Answer 14

A=P((1-(1+r)^-n)/r)

Solved for P

P=455.81

Make sure to do n x 12 and r/12