Noah wants to put $1,000 in a savings account with a 1.5% annual interest rate. How much more money will he have after one year if it is compounded monthly versus no compounding?
simple interest: 1000(1 + 0.015)
compounded: 1000(1 + 0.015/12)^12
now just subtract the results
To find out how much more money Noah will have after one year if the savings account is compounded monthly versus no compounding, we can use the formula for compound interest.
First, let's calculate the result for no compounding. For this case, we would simply multiply the initial amount ($1,000) by the interest rate (1.5%) and then add that amount to the initial amount.
Total amount without compounding = Initial amount + (Initial amount * interest rate)
= $1,000 + ($1,000 * 0.015)
= $1,000 + $15
= $1,015
Now let's calculate the result for monthly compounding. To do this, we need to divide the annual interest rate by 12 to get the monthly interest rate, and the number of times the interest is compounded in a year is 12.
Monthly interest rate = Annual interest rate / Number of compounding periods (12 monthly periods)
= 1.5% / 12
= 0.0125 (or 0.125%)
To calculate the total amount with monthly compounding, we use the formula:
Total amount with monthly compounding = Initial amount * (1 + Monthly interest rate)^Number of compounding periods
Plugging in the values, we have:
Total amount with monthly compounding = $1,000 * (1 + 0.00125)^12
Using a calculator, this gives us:
Total amount with monthly compounding ≈ $1,000 * (1.00125)^12
≈ $1,000 * 1.015
≈ $1,015
So, Noah will have the same amount, $1,015, after one year whether the savings account is compounded monthly or not. Hence, the difference in money will be $0.