AF4: Time value of money Flashcards
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.
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
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.
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
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
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
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%
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
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%
