Given,
The money deposite, P=$1500
The rate of interest is r=3%
Time, n=5 year.
a. The amount after 5 years is,
[tex]A=Pe^{rn}=1500e^{0.03\times5}=1742.75[/tex]
Thus the amount is $1742.75
b. Let time taken to double the money be 2.
Thus, A=2P
So,
[tex]A=Pe^{rt}\Rightarrow2P=Pe^{rt}\Rightarrow2=e^{rt}[/tex]
Taking log we have,
ln2=rt
ln 2=0.03t
t=ln2/0.03=23 years
Thus the answer is 23 years.
