Find the amount of compound interest earned in an account that opens with $27,000, earns 4.6% interest compounded daily, and is held for 25 years. Assume 360 days in a year. (Round your answer to the nearest cent.)
I came up with $85,264.94 is this correct if not I need help!!!
correct.
To find the amount of compound interest earned, you can use the formula:
A = P(1 + r/n)^(nt) - P
Where:
A = the total amount after interest has been applied
P = principal amount (initial deposit)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years
Using the given information:
P = $27,000
r = 4.6% (expressed as 0.046)
n = 360 (since interest is compounded daily)
t = 25
Plugging these values into the formula, we get:
A = 27000(1 + 0.046/360)^(360*25) - 27000
Calculating this using a calculator or a spreadsheet, we find that A is approximately $122,264.94.
To find the amount of compound interest earned, we subtract the principal amount from the total amount:
Compound Interest = A - P = $122,264.94 - $27,000 = $95,264.94
Therefore, the correct amount of compound interest earned is $95,264.94, not $85,264.94.