# A person initially places \$1000 in a saving account... find differential equation

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• Feb 15th 2014, 09:39 PM
crownvicman
A person initially places \$1000 in a saving account... find differential equation
A person initially places \$1000 in a saving account that pays interest at the rate of 1.1% compounded continuously . Suppose the person arranges for \$20 per week to be deposited into the savings account.

a) Write a differential equation for P(t), the amount on deposit after t years (assume weekly deposits is close enough to continuous deposits)

b) Find the amount on deposit after 5 years?

I was already given the answer to a.) as dP/dt= .011P+1040 and b) as \$6,402.20 but I'm not sure how these answers were gotten
I know that the 1040 represents 20 dollars per week and the .011 represents 1.1% over the course of the whole year but I'm not sure where P came in or how to start B at all
• Feb 15th 2014, 09:59 PM
chiro
Re: A person initially places \$1000 in a saving account... find differential equation
Hey crownvicman.

Basically the continuous interest means that the infinitesimal change is the rate times what actually exists which is 0.11 * P.

The idea is that for interest if it is done on a term by term basis, then you will look at your deltas corresponding to the term. So instead of it being infinitesimal, it will be some fixed length quantity corresponding to the term (like a year, month, day, etc). When you make this delta go to zero in the limit, then you get an infinitesimal like in calculus.

Remember that in calculus the differentials represent the changes as they go to zero, but never reach zero.

In the continuous limit you get 11% of what exists which is 0.11 * P and the notion of the limit corresponds with continuous compounding.
• Feb 16th 2014, 10:40 AM
crownvicman
Re: A person initially places \$1000 in a saving account... find differential equation
Thank you very much. I don't know why my question got messed up before, I didn't notice it until just now. It was supposed to say 1.1% per year compounded continuously and \$20 per week is deposited into the saving account.

As for B, I'm sure I keep making a mistake because I still haven;t gotten 6,400