How much interest did she earn? (compound interest)

Given:
Annual compound interest is 10%
Calculation cycle: 4 times a year.
Final sum in account: $600.00 after 4 years.

Let the initial unknown principle sum be #P#
Let the total interest in dollars be #x #
Let the count of years be #n=4#
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#P(1+10/(nxx100))^(4n) =" total in the account"=$600#

As the is a cycle of 4 calculations per year we have the indices of #4n #

This is over 4 years so #n=4# giving:

#P(1+10/(400))^(16) =$600#

#P(410/(400))^(16) =$600#

#P=$600-:(410/400)^(16) = $404.17496... #

Rounding gives: #P=$404.17#

Thus the interest is the difference.

#$600.00#
#ul($404.17 larr" Subtract")#
#$195.83#

Compound interest is given by the formula:

#"FV"="PV"(1+r/n)^(nt)#

Where:

#FV=" future value"#

#PV = " present value"#

#bbr=" interest rate"# ( Given as a decimal )

#bbn= " compounding period"#

#bbt= " time in years"#

We are give interest rate of #10%# so.

#r=10/100=0.1#

compounding period is quarterly so,

#n=4#

Time period is 4 years so:

#t=4#

#FV =600#

To find the amount of interest earned, we first need to find the present value:

Using:

#"FV"="PV"(1+r/n)^(nt)#

#600=PV(1+0.1/4)^16#

#600=PV(1.025)^16#

#PV=600/((1.025)^16)=404.1749600#

Interest earned is:

#FV-PV#

#600-404.1749600=195.8250400#

#$195.83# to nearest cent.