To save for a child's education,the petersen's 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.
2500*((1+.06/365)^(20*365) - 1)
Unless you count leap years.
To find the amount of interest earned on the account over a 20-year period, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the total amount after interest
P is the principal amount (initial deposit)
r is the annual interest rate (in decimal form)
n is the number of times the interest is compounded per year
t is the number of years
Here's how to apply this formula to the given problem:
P = $2500 (initial deposit)
r = 6% per year = 0.06 (in decimal form)
n = 365 (compounded daily)
t = 20 years
Plug in the values into the formula:
A = 2500(1 + 0.06/365)^(365*20)
Now we need to calculate the exponent.
365 * 20 = 7300
So, the expression becomes:
A = 2500(1 + 0.06/365)^(7300)
Let's solve it:
1 + 0.06/365 = 1.00016438356 (approx.)
A = 2500(1.00016438356)^7300
Using a calculator or a computer, calculate the value of (1.00016438356)^7300 and multiply it by 2500. This will give you the total amount (including interest).
Once you have the total amount, subtract the initial principal of $2500 from it. The difference will be the amount of interest earned on the account over the 20-year period.