Question

How much should you invest each month in order to have $800,000 if your rate of return is 5% compounded monthly and you want to achieve your goal in 40 years?

$

How much interest will you earn?

$

How much should you invest each month in order to have $800,000 if you want to achieve your goal in 20 years?

$

If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?

$

Answer 1

Given that,

Amount needed PV = $800000

rate of return r = 5% p.a. compounded monthly

time of investment t = 40 years

compounding frequency n = 12 months

a). monthly saving is calculated using PV formula of annuity,

PMT = PV*(r/n)/(1 - (1+r/n)^(-n*t)) = 800000*(0.05/12)/(1 - (1+0.05/12)^(-12*40)) = $3857.57

Monthly investment PMT = $3857.57

b). interest earned = monthly investment*number of month - amount needed = 3857.57*12*40 - 800000 = $1051634.95

c). If PV = $800000 is needed in t = 20 years.

Monthly saving PMT = 800000*(0.05/12)/(1 - (1+0.05/12)^(-12*20)) = $5279.65

d). If PMT = $5279.65 is invested for t = 10 years,

Saving in 10 years is

PV = 5279.65*(1 - (1+0.05/12)^(-12*10))/(0.05/12) = $497772.15

Amount of saving after 10 years = $497772.15