If I invested 1,000 into an account earing 5% compund interest which was paid monthly, How much would I have after 3 months?
To calculate the amount you would have after 3 months with compound interest, you can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment) = $1,000 in this case
r = the annual interest rate (in decimal form) = 5% = 0.05
n = the number of times interest is compounded per year = 12 (since interest is paid monthly)
t = the number of years = 3 months / 12 months/year = 0.25 years
Now, let's substitute these values into the formula:
A = 1,000(1 + 0.05/12)^(12*0.25)
Simplifying the formula:
A = 1,000(1.00417)^(3)
Using a calculator or a spreadsheet, perform the exponentiation:
A = 1,000(1.01255)
Now, multiply and round to two decimal places:
A ≈ $1,012.55
After 3 months, investing $1,000 at an annual interest rate of 5% compounded monthly, you would have approximately $1,012.55.