Find the total investment and the interest earned when $2,500 is invested at 5% compounded semiannually for 3 years.
P = Po(1+r)^n.
Po = $2,500 = Initial investment.
r = (5%/2)/100% = 0.025 = Semi-APR expressed as a decimal.
n = 2Comp/yr * 3yrs = 6 Compounding periods.
Plug the above values into the given Eq and get:
P = $2899.23
I = P-Po
To find the total investment and the interest earned, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total investment after n years
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount (P) is $2,500, the annual interest rate (r) is 5% (or 0.05 as a decimal), interest is compounded semiannually (n = 2), and the investment period is 3 years (t = 3).
Let's plug the values into the formula and calculate:
A = 2500(1 + 0.05/2)^(2*3)
A = 2500(1 + 0.025)^(6)
A = 2500 * 1.025^6
A ≈ 2500 * 1.1629
A ≈ $2907.25 (rounded to the nearest cent)
The total investment after 3 years would be approximately $2907.25.
To find the interest earned, we can subtract the principal amount from the total investment:
Interest = A - P
Interest = 2907.25 - 2500
Interest ≈ $407.25
So, the interest earned over 3 years would be approximately $407.25.