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?

  • 1
    $\begingroup$ The factor $(1+r)$ comes from the fact that Mary receives her first cheque now and not at the end of the period. $\endgroup$ Apr 19 '19 at 13:56
  • $\begingroup$ Please give a reply if you have any further questions or not. $\endgroup$ Apr 19 '19 at 14:07
  • $\begingroup$ The $R$ is the amount of each payment. The cost of the annuity has to scale with that. $\endgroup$ Apr 19 '19 at 15:03
  • $\begingroup$ 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? $\endgroup$ Oct 16 '20 at 18:11

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


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