大家好。一个问题我一时没法明白，能否请高人指点一下？

Investment Science by David Luenberger
Chapter 2 P.36
#9 (An appraisal) You are considering the purchase of a nice home. It is in every way perfect for you and in excellent condition, except for the roof. The roof has only 5 years of life remaining. A new roof would last 20 years, but would cost $20,000. The house is expected to last forever. Assuming that costs will remain constant and tht the interest rate is 5%, what value would you assign to the existing roof?

书后的答案是 $6,948. 请问这个数字是怎么来的？

多谢！