What is the present value (aka price) of a 20-year, pure discount bond (zero coupon bond) that pays $1000 at maturity if it is priced to yield 7.62% per year (YTM)

The present value / Price of the bond is $230.21

Explanation:

The bond has a future value of 1,000 which means it will pay 1,000 when it matures, also there are no payments in between as this is a pure discount bond. In order to find the present value/price we will have to discount 1000 by the current interest rate and 20 years back.

Present value = Future value / (1+Interest rate) ^N

Future value = 1,000

Interest rate = 7.62%

N = 20

1000 / (1.0762) ^20

PV = 230.21