the interest earned on a $50,000 deposited for six years at 4 1/8% interest compounded continuously is $14040.97
Given :
Amount $50,000 deposited for six years at 4 1/8% interest, compounded continuously.
Compounded continuously formula is
[tex]A=Pe^{rt}[/tex]
Where P is the initial amount deposited
'r' is the rate of interest
t is the time period
A is the amount after 't' years
Lets find out A using the given information
[tex]A=Pe^{rt}\\P=50000\\r=4\frac{1}{8} =\frac{33}{8} \\[/tex]
Divide by 100 to remove %
[tex]r=0.04125\\t=6[/tex]
Substitute all the values
[tex]A=50000e^{0.04125\cdot \:6}\\A=50000e^{0.2475}\\A=64040.96811.....[/tex]
Now we find out the interest
I=A-P
[tex]Interest = 64040.96811-50000=14040.9681[/tex]
Interest = $14040.97
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