# Differential Equation (Deposit)

1. Dec 6, 2009

### mybingbinghk

1. The problem statement, all variables and given/known data

A person initially place $500 in a saving account that pays interest at the rate of 4% per year compounded continuously. Suppose the person arranges for$10 per
week to be deposited automatically into the savings account.
(I) Write a differential equation for P (t), the amount on deposit after t years
(assume that “weekly deposits” is close enough to “continuous deposits” so
that we may model the balance with a differential equation.)

2. Relevant equations

Let X(t) be the amount on deposit after t years and dX/dt be the rate of change of the deposit.

3. The attempt at a solution

dX/dt = 0.04X +480 (480 is the amount of deposit yearly)
and
X(t) = C e^0.04t +480t , where C is a constant

Let X(0) = C =500, then
P(t)=500e^0.04t+480t

Acturally, I dun no the approach is correct or not? Pls Help!