Question

The accumulated savings of an engineer on the verge of retirement, amounting to $100,000, are in an account paying 6% compounded quarterly. The engineer wishes to withdraw $6,000 each quarter. For how long can she withdraw the full amount?

Answer 1

this can be known using present value of annuity formula

present value of annuity = A* [1 - (1+r)^(-n)]/r

here,

present value of annuity = 100,000

A =6,00

r = 6% =>0.06 per annum =>0.06/4 =>0.015 per quarter.

n = to be found out.

=>100,000 = 6,000[1-(1.015)^(-n)]/0.015

=>1500 =6000[1-(1.015)^(-n)]

=>0.25 =1-1.015^(-n)

=>1.015 (-n) = 0.75

apply logarithms on both sides.

=>(-n) log (1.015) = log (0.75)

=>(-n) (0.006466042) = -0.1249387

=>n=19.322284 quarters.

=>n = 4.830571 years

=>4.83 years.