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1

 

What do we mean by the time value of money?

 

 

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In simple terms, it is about how we calculate the future value of an investment, or

how we work back from a future required value to calculate the present value.

2

 

Compounding is where we take the known present value and use this to calculate a the potential future value.

 

For example, John has invested £50,000 into his investment and wants to know, assuming 5% net, what this will be worth in 10 years time when he retires.

What would the formula look like?

 

The formula:

FV = PV (1+r)n

Where:

FV = Future value

PV = Present value

r = Rate of return

n = Number of years

3

 

Using John as an example, what would his investment be worth in 10 years time?

 

FV =  PV x (1 + 0.05)10

 

FV = £50,000 x (1.05)10

FV= £50,00 x 1.6289

FV = £81,445

 

In AF4, you are recommended to have a financial /scientific calculator. You should have this before your course and be familiar with undertaking a calculation such as this.

4

 

Discounting is working from a known future value to determine the present value.

 

For example, Janet wants to provide university fees of £15,000 to her grandaughter in 12 years time. Assuming a 3% net return, how much must she invest now?

 

What would the formula look like? I'll give you a clue, it uses all of the same elements as the compounding  formula but in a different order.

 

Discounting formula:

                                          PV =    FV  

                                                     (1+r)n

 

Where:

PV = Present value

FV = Future value

r= Rate of retiurn

n = Number of years

5

 

Example. How much does Janet need to invest today for her grandchild's university fees?

 

If you don't have a calculator, work your way through the steps to the process required.

                                             PV =      FV  

                                                          (1+r)n

                                             PV = £15,000

                                                       (1+03)12 

                                             PV = £15,000

                                                        1.4258

                                             PV=  £10,520

6

How do we find the annual compound interest rate when we know the present and future value along with the time frame?

 

r = [(FV / PV)1/n - 1] x 100

•FV = Future value
•PV = Present value
•r = Interest rate as a decimal e.g. 4% = 0.04
•n = Number of years

7

Kate requires £35,000 in 12 years time for little Hugo’s university fees. She has £21,000 available to invest now. What annual rate of return will be required to reach her goal?

 

 

If you don't have a calculator, work your way through the steps to the process required.

 

 

r = [(FV / PV)1/n - 1] x  100

 

r = [(£35,000 / £21,000)1/12 - 1] x  100
r = [1.6671/12 - 1] x  100
r = [1.0435 - 1] x  100

r = 4.35%

8

How do we find the Annual Effective Rate (AER) when there are more than one payments in a year?

 

AER = [(1 + r/n)n - 1] x  100

FV = Future value
PV = Present value
r = Nominal interest rate
n = Number of payments made in a year

9

Best Bank pays a nominal interest of 3.2% gross per annum, paid monthly. Calculate, showing all your workings, the Annual Effective Rate (AER).

 

If you don't have a calculator, work your way through the steps to the process required.

 

 

Best Bank:

AER = [(1 + r/n)n - 1] x  100

(1 + 0.032 / 12)12 – 1 x 100

 (1.03247)12 – 1   x 100

=  3.25%