Question

a person places rm20,000 in a saving account which pays 5 percent interest per annum , compounded continuously.
a)derive a differential equation that model the initial-value problem
b)find the solution of the differential equation
c)find the amount in the account after three years
d)find the time required for the account to double in value,presuming no withdrawal and no additional deposits

Answer 1

Well, do it!

A = Savings Account Balance
t = time
We seek A(t)

Continuous compounding suggests: \(\dfrac{dA}{dt} = What?\)

Hint: The change in account value is proportional to the account value.

Answer 2

dA/dt is 0.05A right ?
and the A initial is 20000 ?

Answer 3

A(0) = 20000. That is right.

Solve away! It's separable: \(\dfrac{dA(t)}{A(t)} = 0.05\cdot dt\)

Answer 4

after that i got A(t)=\[\sqrt{0.1t}\]

Answer 5

?? How did you get a square root? You should get a logarithm.

Answer 6

\(\log\left(A(t)\right) = 0.05\cdot t + C\)

Answer 7

so the final equation is
\[A(t)=20000e^{0.05t}\]

Answer 8

The \(A(t) = Ce^{0.05t}\)

We know that \(A(0) = Ce^{0.05(0)} = C = 20000\)

And we are done. Good work.

Answer 9

thx so much for your help..
really appreciate it xD