Question

Suppose a women decided to retire as soon as she saved 800,000. Her plan is to put 550 each month into an ordinary annuity that pays an annual interest of 4.1 percent. In how many years will she be able to retire?

Answer 1

this can be known using future value of annuity formula;

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

here,

future value of annuity = 800,000

A = 550

r= 4.1 % per annum

=>4.1%*1/12 =>0.341667% per month

=>0.00341667.

n= to be found out.

800,000=550*[(1.00341667)^(n)-1]/0.00341667

=>2,733.336 = 550*[(1.00341667)^n-1]

=>4.96970181818= (1.00341667)^n-1

=>5.96970181818 = (1.00341667)^n

apply logarithms in both sides,

=> log (5.96970181818) = log (1.00341667)^n

=>0.77595264= n* log (1.00341667)

=>0.77595264 = n *0.001481312

=>n = 0.77595264 / 0.001481312

=>523.827958 months

=>523.827958 / 12 months =>43.65 years.

so she will be able to retire in 43.65 years.