# Annuities, lottery and interest rate

I am having trouble doing this question.

Mary Jones won $$\4,000,000$$ in a state lottery.

She will receive a cheque for $$\200,000$$ now and a similar one for each year for 19 years. To provide these 20 payments, the State Lottery Commission purchased an annuity due at the interest rate of $$10\%$$ compounded annually. How much did the annuity cost the Commission?

The answer key is utilizing this formula:

$$A =R\cdot (1+r)\cdot \frac{1 – (1+r)^{-n} }{ r}$$

However, I am wondering, where did $$R\cdot (1+r)$$ come from?

• The factor $(1+r)$ comes from the fact that Mary receives her first cheque now and not at the end of the period. Apr 19 '19 at 13:56
• Please give a reply if you have any further questions or not. Apr 19 '19 at 14:07
• The $R$ is the amount of each payment. The cost of the annuity has to scale with that. Apr 19 '19 at 15:03
• You are having trouble doing this question? What do you mean? Are you trying to find out where did R x (1 + r) come from? Oct 16 '20 at 18:11