TIME VALUE OF MONEY Flashcards
What do we mean by the time value of money?
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%
