Elizabeth is seeking to expand her rare coin collection. Each year, rare coins increase in price at a three percent rate. She believes that if she invests her money for one year, she should be able to buy 26 coins for what 25 coins would cost today. What is her real interest rate or reward for waiting?

Question

Quizplus · Accepted Answer

Let X be the current cost of 25 coins. Then, the cost of 26 coins after one year is 1.03X (due to an increase in price). Elizabeth believes that she will be able to buy 26 coins for the same price as 25 coins today, so she must have 1.03X = X, which means X = 1.03X/26. Solving for X gives X = $38.99. Therefore, the real interest rate or reward for waiting is (1.03X - X)/X = 0.03, or 3.00%. The closest answer choice is A, which is 4.00% - so it's the best choice.

Elizabeth Is Seeking to Expand Her Rare Coin Collection