After five years of earning interest at an annual rate of 4%, an investment has earned $1,200 in interest. Determine the amount of the initial investment. Show all work for full credit.
I am assuming this is compound interest at 4% of the value at the beginning of the year and that no money is withdrawn or added over the time period.
The formula for the amount in the account at the end of the time will be: [tex]A = P * (1.04)^5[/tex] Where A is the amount at the end and P is the initial investment.
Therefore we have that the interest earned is: [tex]I = P * (1.04)^5 - P[/tex] Where I is the interest earned.
We can factorise to get: [tex]I = P * ((1.04)^5 - 1)[/tex] And then divide to find P. [tex]P = \frac{I}{(1.04)^5 - 1} [/tex]
And now substituting I = $1200 into this we get: P = $5538.81 (2 d.p.)
