Mathematical Methods in the Physical Sciences · Problem 1.14

INFINITE SERIES, POWER SERIES — Mary Boas

Mathematics — Methods · geometric-series

Problem

A dollar due to be paid to you at the end of

n

months, with the same interest rate as in Problem 13, is worth only

(1.005)^{-n}

dollars now (because that is what will amount to \

1 after

months). How much must you deposit now in order to be able to withdraw

10 a month forever (starting one month from now)? (Assume the interest rate remains the same forever.)