Josh bought a bond with a par value of 1,500 from company ABC. The bond pays twenty annual coupons of 90 and matures at the end of twenty years. It is bought and redeemed at par.

Immediately after his purchase, company ABC issues another bond with the same coupon structure and redemption value as the par bond, but with a lower annual effective yield rate of 4%.

Josh calculates the price of the new bond using the first-order modified approximation and the first-order Macaulay approximation. Let X be the new price using the first-order Macaulay approximation and let Y be the new price using the first-order modified approximation.

Calculate XY.