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?
Correct me if Im wrong. R=Rent, r=number of payments of R in a year, n=total time in years.
Then the resolution might be A =200,000\cdot (1+1)\cdot \frac{1 – (1+1)^{-20} }{ 1}
A = 399,999.62