Good day to you.
How can I approach this math problem.
"To save for a child's education, the Petersens deposited $2500 into an account that pays 6% annual interest compounded daily. Find the amount of interest earned on this account over a 20-year period".
I try solving with the formula:
A=(1+ i/m)^mt. m = 365; but cannot arrive at the correct answer.
Thanks.
Good day! I'd be happy to help you solve this math problem.
To solve for the amount of interest earned on the account over a 20-year period, we'll need to use the formula for compound interest:
A = P(1 + r/n)^(nt) - P
Where:
A = Final amount (including interest)
P = Principal amount (initial deposit)
r = Annual interest rate (decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case, the principal amount (P) is $2500, the annual interest rate (r) is 6% (or 0.06 as a decimal), the number of times interest is compounded per year (n) is 365 (since interest is compounded daily), and the number of years (t) is 20.
Using the formula, we can calculate the amount of interest earned on the account:
A = 2500(1 + 0.06/365)^(365*20) - 2500
Now, let's simplify the equation and calculate the value:
A ≈ 2500(1 + 0.000164)^(7300) - 2500
A ≈ 2500(1.000164)^(7300) - 2500
A ≈ 2500(2.963768) - 2500
A ≈ 7409.42 - 2500
A ≈ 4909.42
Therefore, the amount of interest earned on the account over a 20-year period is approximately $4909.42.
Remember, when using the formula for compound interest, it's important to correctly substitute the values and calculate them accurately to arrive at the correct answer.