Interest problem

Hello, Jared!

I am trying to find the interest earned on $10,000 invested for 7 years at 6.1 % interest compounded monthly.

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The formula is: \(\displaystyle \,A\;=\;P(1\,+\,i)^n\)

where \(\displaystyle P\) = principal invested,
. . . . . . \(\displaystyle i\) = interest rate per period,
. . . . . . \(\displaystyle n\) = number of periods,
. .and \(\displaystyle A\) = final value (Amount) of the investment.

Your preliminary work is correct. \(\displaystyle \;\)Since the periods are monthly,
\(\displaystyle \;\;\)7 years = 84 months . . . \(\displaystyle n\,=\,84\).

We are given an interest rate of 6.1% (annual).
Then the interest per month is: \(\displaystyle \,i\:=\:\frac{6.1\%}{12}\,=\,\frac{0.061}{12}\)

Substitute those values into the formula:

\(\displaystyle \;\;A\;=\;1000\left(1\,+\,\frac{0.061}{12}\right)^{84} \;=\;1000(1.530995798)=\;1530.995798\)

The investment will be worth $1531 at the end of the seven years.

Therefore, it will have earned $531 in interest.

The magic formula is
x=P(1+i)^t where P is the amount invested, i is the interest per period and t is the number of periods.
6.1% per year = 6.1/12 per month (period) for 84 months.