Question 1194734: You would like to have $900,000 when you retire in 35 years. How much should you invest each quarter if you can earn a rate of 5.4% compounded quarterly?
Found 2 solutions by Theo, math_tutor2020:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you would need to invest 2194.65 at the end of each quarter.
you can use the calculator at https://arachnoid.com/finance/index.html to confirm.
results from using this calculator are shown below:
inputs are everything except pmt.
output is pmt.
you would set pv to 0, fv to 900,000, np to 35 years * 4 quarters per year = 140, interest rate per quarter = 5.4% per year / 4 = 1.35% per quarter, payments are made at the end of each quarter.
let me know if you have any questions.
theo
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
We'll be using a future value of an annuity
The formula is
FV = P*( (1+i)^n - 1 )/i
We'll be using the ordinary annuity and not the "annuity due" variation.
FV = future value
P = payment per period
i = interest rate per period (in decimal form)
n = number of periods
In this case, each period is one quarter (aka 3 months, since 12/4 = 3).
We know the following:
FV = 900,000 = amount we want at a later future date
i = 0.054/4 = 0.0135 which is exact
n = 35*4 = 140 quarters
Let's solve for P.
FV = P*( (1+i)^n - 1 )/i
900,000 = P*( (1+0.0135)^140 - 1 )/0.0135
900,000 = P*410.088990826382
P = (900,000)/410.088990826382
P = 2194.64560164462
P = 2194.65
Answer: You should deposit $2,194.65 at the end of each quarter, do so for 140 quarters (aka 35 years), to accumulate $900,000 which is composed of the deposits plus added interest.
The tutor @Theo offers a great calculator to check your answer. The answer is highlighted in red in their screenshot; however, the payment amount should be a positive number.
|
|
|
