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 $21,200 a year for 20 years is provided. The actual cost to the publisher to purchase an annuity to pay for the prize is $180,000. What interest rate (to the nearest percent) was used to determine the amount of the annuity? (Assume end-of-year payments.) (Round factor values to 5 decimal places, e.g. 1.25124.) Click here to view factor tables Interest rate %

Answer 1

Present value of Price money to be paid in future = $180,000

Yearly amount to be paid= $21,200

Factor = $180,000 / $21,200 = 8.4906 . Let's see 8.4906 in Cumulative PVF table in 20 years . It will fall between 10% and 11%.

Let's see PVF of $1 for 20 year @10% = 8.51356

PV of price to be paid in future = $21,200 * 8.51356 = $180,487

PVF of $1 for 20 year @11% = 7.96333

PV of price to be paid in future = $21,200 * 7.96332= $168,822

Let's calculate the rate at which PV would be 180,000.

10% + ($180,487 - $180,000) / ($180,487 - $168,822) * 1%

10% + 0.0396%

= 10.0396%