Example $2\mathrm{.}14$: Calculating the present value of an annuity due at $12\%$

An investor wants to buy an annuity of R$100$ for the next three years, each instalment being paid at the beginning of the year. If a bank is prepared to pay interest at $12\%,$ how much must be invested today?

It can be seen that the amount will be invested and the first instalment will immediately be repaid. It can be illustrated as shown in Table $2\mathrm{.}6.$