Applications of the First Order ODE

Question

MARC · Answer

(Compounded Interest) 
Upon the birth of their first child, a couple deposited RM 5000 in an account that pays 8% interest compounded continuously. The interest payments are allowed to accumulate. How much will the account contain on the child’s eighteenth birthday ?

MARC · Answer

$P=Ae^{kt}$

$t=0,P_0=5000$
$t=1,P_1=5400$

$5000=Ae^{k(0)}$
$A=5000$

$P=5000e^{kt}$

$5400=5000e^{k(1)}$

$\frac{27}{25}=e^k$

$k=0.07696$

$P=5000e^{0.07696t}$

$t=18,P_{18}=?$

$P_{18}=5000e^{0.07696(18)}$

$P_{18}=19979.72$

Answer supposed to be $21103.48$ but got a different answer >.<

dude · Answer

$5000e^{\large 0.08\times 18}\approx  21103.47908 ~or~ 21103.48$

The rate is 8%, so it is just 0.08 times 18 in the exponent xD

MARC · Answer

yeah,got it bro,haha
Thanks dude ;)