Calculate the amount of interest earned in 10 years on 1000.00 invested at 3.00% per annum, compounded monthly.
P = Po(1+r)^n
Po = $1000.
r = (3%/12)/100% = 0.0025 = Monthly %
rate expressed as a decimal.
n = 10yrs. * 12Comp/yr = 120 Compounding
periods.
Plug the above values into the given Eq
and solve for P.
I = P - Po
To calculate the amount of interest earned on an investment over a given period, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the future value of the investment including the interest
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case, we have:
P = $1000.00 (initial investment)
r = 3.00% per annum (or 0.03 in decimal form)
n = 12 (compounded monthly)
t = 10 years
Plugging in these values into the formula:
A = 1000(1 + 0.03/12)^(12*10)
Now we can calculate A:
A = 1000(1 + 0.0025)^(120)
A ≈ 1000(1.0025)^(120)
A ≈ 1000(1.34392)
A ≈ $1343.92
To find the interest earned, we can subtract the initial investment from the future value:
Interest earned = A - P
Interest earned = $1343.92 - $1000.00
Interest earned ≈ $343.92
Therefore, the amount of interest earned in 10 years on an investment of $1000.00 at a 3.00% annual interest rate compounded monthly is approximately $343.92.