Question

suppose a woman has decided to retireas soon as she has saved $1,000,000. her plan is to put $600 each month into the ordinary annuity that pays an annual interest rate of 4.4%. in how many years will ahe be able to retire? (round to the nearest year as needed).

Answer 1

Data given:

Amount of each monthly annuity payment, M = $600

Rate of interest per annum, r = 4.4%

Future value of ordinary annuity, FV = $1000000

Time period of investment (in years), t = ?

Frequency of payments in a year, n = 12

As we know, the formula for computing the future value of an ordinary annuity is given as -

where M - amount of each annuity payment

r - rate of interest per annum

n - frequency of payments in a year

t - time period through which payments are made

Using the above formula, we can compute the time period (number of years by which the woman can retire) as -

On taking logarithm on both sides, we get -

  

Thus, the time required for the woman to retire will be approximately 45 years (rounded to the nearest year).