Financial Markets Arithmetic
Simple and compound interest
A loan that has one interest payment on maturity is accruing simple interest. On short-term instruments there is usually only the one interest payment on maturity, hence simple interest is received when the instrument expires. The terminal value of an investment with simple interest is given by A1.1 below.
F is the terminal value or future value
P is the initial investment or present value
r is the interest rate
So for example if P is £100, r is 5% and the investment is one year then
F = 100 (1 + 0.1)
The market convention is to quote interest rates as annualised interest rates, which is the interest that is earned if the investment term is one year. Consider a three-month deposit of £100 in a bank, placed at a rate of interest of 6%. In such an example the bank deposit will earn 6% interest for a period of 90 days. As the annual interest gain would be £6, the investor will expect to receive a proportion of this, which is calculated below:
Therefore the investor will receive £1.479 interest at the end of the term. The total proceeds after the three months is therefore £100 plus £1.479. If we wish to calculate the terminal value of a short-term investment that is accruing simple ...