Question

Question:In a book named Treasure, the reader has to figure out where a 2.2 pound, 24 kt gold horse has been buried. If the horse is found, a prize of \(25,000 a year for 20 years is provided. The actual cost to the publisher to purchase an annuity to pay for the prize is \)245,000. What interest rate (to the nearest percent) was used to determine the amount of the annuity? (Assume end-of-year payments.)

Short answer

An annuity is closest to 9.8%

Step-by-step solution

Step-by-Step SolutionStep 1 Interest Rate definition

Interest rate is the amount that is charged or paid on the amount of money owed or borrowed.

Calculation of Annuity

$\begin{array}{rcl}\mathbf{Present}\mathbf{}\mathbf{}\mathbf{Value}& \mathbf{=}& \mathbf{Present}\mathbf{}\mathbf{}\mathbf{value}\mathbf{}\mathbf{}\mathbf{of}\mathbf{}\mathbf{}\mathbf{an}\mathbf{}\mathbf{}\mathbf{ordinary}\mathbf{}\mathbf{}\mathbf{annuity}\mathbf{}\mathbf{}\mathbf{of}\mathbf{}\mathbf{}\mathbf{\$}\mathbf{25000}\mathbf{}\mathbf{for}\mathbf{}\mathbf{}\mathbf{20}\mathbf{}\mathbf{periods}\mathbf{}\mathbf{at}\mathbf{}\mathbf{percent}\\ \mathbf{Present}\mathbf{}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{an}\mathbf{}\mathbf{ordinary}\mathbf{}\mathbf{annuity}\mathbf{}\mathbf{of}\mathbf{}\mathbf{\$}\mathbf{25000}\mathbf{}\mathbf{for}\mathbf{}\mathbf{20}\mathbf{periods}\mathbf{}\mathbf{at}\mathbf{}\mathbf{percent}& \mathbf{=}& \frac{\mathbf{245000}}{\mathbf{25000}}\\ & \mathbf{=}& \mathbf{9}\mathbf{.}\mathbf{8}\\ & & \end{array}$