A company deposits

Question

A company deposits $5,000 into an account that earns interest. The rate at which the account value changes is given by dA/dt = 0.0225A

where A(t) is the account value, in dollars, after t years. What will be the value of the account after 10 years if no additional deposits or withdrawals are made?

$5,112.50

$5,113.78

$6,246.02

$6,261.61

Answer 1

Hi,

dA/dt = 0.0225A both sides divide by A and time dt

dA/A = 0.0225 dt then integral of both sides

Ln A = 0.0225 t ====> A(t) = e^0.0225t

On the other word, A (t) = 5000 e ^rt=====> A(t) = 5000 e ^0.0225t

A(10) = 5000 e ^0.0225(10)

A(10) = 6261.61

I hope it is useful,

Minoo

Answer 2

The answer is $6,261.61.

First solve the differential equation:

dA/dt = 0.0225A ===> dA/A = 0.0225 dt ===> A(t) = A(0) . e^{0.0225 t}

therefore A(t=10) = 5000 . e^{0.0225 * 10} = 6,261.61.