You invest $5000 at 3% compounded monthly for 15 years. How much interest will you earn?
P = Po * (1+r)^n
r = (3%/12)/100% = 0.0025 = Monthly %
rate expressed as a decimal.
n = 12Comp./yr * 15 yrs. = 180 Compounding periods.
Solve for P.
I = P-Po
To calculate the interest earned on an investment, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
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 the money is invested for
In this case:
P = $5000
r = 3% = 0.03 (since the interest rate is given as a percentage, we divide it by 100 to convert it to decimal form)
n = 12 (interest is compounded monthly, so there are 12 compounding periods in a year)
t = 15 years
Now, we can plug these values into the formula and solve for A:
A = 5000 * (1 + 0.03/12)^(12*15)
Using a calculator or spreadsheet, we can evaluate the expression to find the future value (A) of the investment after 15 years. Subtracting the initial principal amount (P) from this future value will give us the total interest earned.