Evan invests money in an account paying a simple interest of 2% per year. If no money will be added or removed from the investment, what should he multiply his current balance by to find his total balance in a year in one step?Answer:
Q. Evan invests money in an account paying a simple interest of 2% per year. If no money will be added or removed from the investment, what should he multiply his current balance by to find his total balance in a year in one step?Answer:
Calculate Simple Interest: To find the total balance after one year with simple interest, we need to calculate the interest earned and add it to the original balance. The formula for simple interest is I=P×r×t, where I is the interest, P is the principal amount (initial investment), r is the annual interest rate (as a decimal), and t is the time in years.
Convert Annual Rate to Decimal: Since Evan's annual interest rate is 2%, we convert this percentage to a decimal by dividing by 100. So, r=1002=0.02.
Determine Time Period: The time t is 1 year, as we are looking for the total balance after one year.
Calculate Interest Earned: Now, we can calculate the interest earned in one year. Using the formula I=P×r×t, we get I=P×0.02×1.
Calculate Interest Amount: The interest earned in one year is 2% of the principal amount, which means Evan should multiply his current balance by 0.02 to find the interest earned.
Find Total Balance: To find the total balance, Evan needs to add the original principal amount to the interest earned. This means he should multiply his current balance by 1 (to account for the original balance) and then add the interest earned (2% of the balance). So, the total balance can be found by multiplying the current balance by 1.02 (1+0.02).
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