house payment series problem

[thebenji]

I think this problem needs to be solved with series...

Steve and Kate want to purchase a house. Suppose they invest dollars per month into a mutual fund. How much will they have for a downpayment after years if the per annum rate of return of the mutual fund is assumed to be percent compounded monthly?

How do I set this up? I know that A=A(0) * (1+r/n)^n

 

[thebenji]

:?: I don't know what happened to the numbers...

Steve and Kate want to purchase a house. Suppose they invest 600 dollars per month into a mutual fund. How much will they have for a downpayment after 9 years if the per annum rate of return of the mutual fund is assumed to be 11 percent compounded monthly?

 

[soroban]

Hello, thebenji!

Hmmm, this is not a Calculus problem . . .

Steve and Kate want to purchase a house.
Suppose they invest 600 dollars per month into a mutual fund.
How much will they have for a downpayment after 9 years
if the return of the mutual fund is 11% compounded monthly?

This is an annuity ... for which there is a formula.

\(\displaystyle \L A \;= \;D\,\frac{(1\,+\,i)^n\,-\,1}{i}\;\;\;\) where: \(\displaystyle \,\begin{array}{ccc}D & = & \text{periodic deposit} \\ i & = & \text{periodic interest rate}\\ n & = & \text{number of periods}\\ A & = & \text{final amount}\end{array}\)


Your problem has: \(\displaystyle D\,=\,600,\;i\,=\,\frac{0.11}{12},\;n\,=\,108\)

Then: \(\displaystyle \L\:A\;=\;600\,\frac{\left(1\,+\,\frac{0.11}{12}\right)^{108}\,-\,1}{\frac{0.11}{12}} \;\approx\;\$109,906.33\)


If you are expected to derive the Annuity Formula, it is a messy problem,
. . but it does not require any Calculus.

 

[thebenji]

Thanks! Yes, in my mind I was expecting to derive a formula like the annuity formula. It makes sense.