Julio invests $6,100 into an account that earns 5.2% annual compound interest. If Julio makes no additional deposits or withdrawals, which best represents the amount of interest Julio will earn after 8 years?
Question
Julio invests $6,100 into an account that earns 5.2% annual compound interest. If Julio makes no additional deposits or withdrawals, which best represents the amount of interest Julio will earn after 8 years?
Solution
To calculate the amount of interest Julio will earn after 8 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 = principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years
In this case, Julio's principal amount (P) is $6,100, the annual interest rate (r) is 5.2% or 0.052 in decimal form, the number of times that interest is compounded per year (n) is assumed to be 1 (annually), and the time the money is invested for (t) is 8 years.
So, we can substitute these values into the formula:
A = $6,100 (1 + 0.052/1)^(1*8)
Solving the equation will give us the total amount in the account after 8 years. To find the interest earned, we subtract the initial principal from this total amount.
Let's calculate:
A = 6,100 * (1.052)^8 A = 9,081.67
So, the total amount in the account after 8 years is $9,081.67.
To find the interest earned, we subtract the initial principal from this total amount:
Interest Earned = A - P Interest Earned = 6,100 Interest Earned = $2,981.67
So, Julio will earn approximately $2,981.67 in interest after 8 years.
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