05. Time value of money

Question 1

What is the formula for calculating the real rate of return?

Answer 1

RREAL = RNOM - RINF

where:
- RREAL = real return
- RNOM = nominal return
- RINF = rate of inflation

Alternate?

(1+Rate of return) / (1+Rate of inflation) - 1 *100

Question 2

What is the formula for calculating a future value?

Answer 2

FV = PV (1 + r)n

Where:
- PV = present value, the original sum invested
- r = interest rate/rate of return as a decimal
- n = no. of time periods
- FV = the future value, the sum accumulated after n periods

Question 3

What is the formula for calculating a future value when there is a change to the compounding rate?

Answer 3

FV = PV x (1 + r1)n1 x (1 + r2)n2

Question 4

How do you calculate 10% interest payable on £1,000 at these different intervals:

• annual interest
• half-yearly interest
• quarterly interest

Answer 4

• £1,000 x 1.10
• £1,000 x 1.05 x 1.05
  i.e. £1,000 x (1.05)2
• £1,000 x 1.025 x 1.025 x 1.025 x 1.025
  i.e. £1,000 x (1.025)4

Question 5

What is the formula for calculating a present value?

Answer 5

PV = FV / (1+r)n

where:
- PV = present value (the sum required now)
- FV = future value (the sum required in the future)
- r = interest rate/rate of return expressed as a decimal
- n = no. of time periods available for investment

Question 6

Annual Percentage Rate (APR) is generally used for ___ and Annual Equivalent Rate (AER) for ___.

Answer 6

• loans
• deposits

Question 7

What does the AER enable?

Answer 7

Comparison of accounts where interest compounds at different rates.

Question 8

What is the formula for calculating the APR / AER / EAR?

Answer 8

= (1 + r/n )n -1 x 100

where:
- r = nominal rate of interest
- n = number of payments

Question 9

What is the formula for calculating the annualised portfolio return?

Answer 9

An = [ (A ÷ P)1/n -1] x 100

where:
- An = annualised return
- n = no. of years invested
- A = total amount accumulated
- P = original amount invested

Question 10

How to calculate an accumulated amount from a regular payment paid in arrears over a given period?

Answer 10

FV = P x

(1 + r)n - 1
___________

    r

where:
P = the regular payment