Calculate the amount of interest earned in 10 years on $1000 invested at 3% per annum, compounded monthly.

how to solve please show me step by step thank you

I will assume you are familiar with the basic compound interest formulas

i = .03/12 = .0025
n = 10(12) = 120

amount = 1000( 1.0025^120 - 1)/.0025
= ....

oops, I misread the question as investing 1000 every month, so

amount = 1000(1.0025)^120
= $1349.35

To calculate the amount of interest earned in 10 years on $1000 invested at 3% per annum, compounded monthly, you can 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 = the annual interest rate (in decimal form)
n = the number of times the interest is compounded in a year
t = the number of years

In this case:
P = $1000
r = 3% or 0.03 (in decimal form)
n = 12 (compounded monthly)
t = 10 years

Let's plug these values into the formula:

A = 1000(1 + 0.03/12)^(12*10)
A = 1000(1 + 0.0025)^(120)
A = 1000(1.0025)^(120)
A ≈ 1000(1.349858807576003)
A ≈ $1349.86

To calculate the amount of interest earned, subtract the initial investment from the future value:

Interest earned = A - P
Interest earned = $1349.86 - $1000
Interest earned ≈ $349.86

Therefore, the amount of interest earned in 10 years on $1000 invested at 3% per annum, compounded monthly, is approximately $349.86.

To calculate the amount of interest earned on $1000 invested at 3% per annum, compounded monthly over 10 years, you can use the formula for compound interest:

A = P (1 + r/n)^(nt)

Where:
A = The final amount
P = The principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years

Let's calculate step by step:

Step 1: Convert the annual interest rate to a decimal.
The annual interest rate is 3%, so divide it by 100: 3/100 = 0.03.

Step 2: Identify the variables in the formula.
P = $1000 (the principal amount)
r = 0.03 (as a decimal)
n = 12 (since interest is compounded monthly)
t = 10 (10 years)

Step 3: Plug the values into the formula and calculate.
A = $1000 (1 + 0.03/12)^(12*10)
A = $1000 (1 + 0.0025)^(120)
A = $1000 (1.0025)^(120)

Now, using a calculator or a spreadsheet, raise 1.0025 to the power of 120 and multiply the result by $1000 to find the final amount.

Step 4: Calculate the final amount.
A = $1000 * (1.0025)^120
A ≈ $1343.92

Step 5: Calculate the interest earned by subtracting the principal amount from the final amount.
Interest earned = $1343.92 - $1000
Interest earned ≈ $343.92

Therefore, the amount of interest earned over 10 years on $1000 invested at 3% per annum, compounded monthly, would be approximately $343.92.