# Jia has just won a R20 million lottery, which will pay her R1 million at the end of each year for...

## Question:

Jia has just won a R20 million lottery, which will pay her R1 million at the end of each year for 20 years. An investor has offered her R10 million for this annuity. She estimates that she can earn 10 percent interest, compounded annually, on any amounts she invests. She asks for your advice on whether to accept or reject the offer. What will you tell her? (Ignore Taxes)

## Annuity:

An annuity is a series of payments of a fixed amount. Individuals pay a series of payments or invested lumpsum amounts to receive annuity periodically over the period. The purpose of an annuity is to provide regular income after retirement.

## Answer and Explanation: 1

Calculation of present value of the annuity

{eq}\begin{align*} {\rm\text{Present Value of Annuity}} &= PMT\left( {\frac{{1 - {{\left( {1 + r} \right)}^{ - n}}}}{r}} \right)\\ &= {\rm{R}}1,000,000\left( {\frac{{1 - {{\left( {1 + 0.1} \right)}^{ - 20}}}}{{0.1}}} \right)\\ &= {\rm{R}} 8,514,000 \end{align*} {/eq}

The present value of an annuity of $8,514,000 is lower than the offered value of an annuity of $1,000,000; Jia should accept the offer.

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Chapter 2 / Lesson 7An annuity is a fixed amount of income paid at regular intervals, such as monthly or quarterly. Learn the definition and formula for annuity, review examples of annuities, and understand how to determine the value of annuities.