A prizewinner can choose Prize A $2000 per year

Question

A prizewinner can choose prize A, $2000 per year for 15 years, or Prize B, 3 cents the first year, with the amount tripling each year through the fifteenth year. Which prize is more evaluable? Howbmuch is IT worth?

Answer 1

Prize A is straightforward to figure out, $2000 per year for 15 years is

$2000*15 = $30,000

For Prize B, you are given that you get 3 cents (= $0.03) for the first year, then it triples each year for the next 14 years.

This can be expressed as $0.03 * 3^14 (3 raised to the 14th power)

3^14 = 4,782,969. Multiplying by the original three cents gives the final total

$0.03 * 4782969 = $143,489.70 Clearly Prize B is more valuable