As a savings plan for college, when Arwyne was born, his parents deposited $25,207 in an account paying 6% compounded annually. How much is the interest earned from this investment after 18 years? Do not round off values in intermediate calculations.Round off only the final answer to the nearest dollar.Do not include currency sign in the answer.Number format: [Ex. 2,540]-No space between numbers-Use comma as thousands separator
Question
As a savings plan for college, when Arwyne was born, his parents deposited $25,207 in an account paying 6% compounded annually. How much is the interest earned from this investment after 18 years? Do not round off values in intermediate calculations.Round off only the final answer to the nearest dollar.Do not include currency sign in the answer.Number format: [Ex. 2,540]-No space between numbers-Use comma as thousands separator
Solution
To calculate the interest earned from this investment after 18 years, we first need to calculate the total amount in the account after 18 years. We can use the formula for compound interest, which is:
A = P(1 + r/n)^(nt)
where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = the time the money is invested for in years
In this case, P = $25,207, r = 6% or 0.06 (in decimal), n = 1 (since the interest is compounded annually), and t = 18 years.
So,
A = 25,207(1 + 0.06)^18 A = $25,207 * 1.06^18
Now, calculate the value of A.
After finding the total amount A, we subtract the initial principal P to find the interest earned.
Interest Earned = A - P
Now, calculate the interest earned and round off the final answer to the nearest dollar.
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