Find the amount of compound interest earned in an account that opens with $27,000, earns 5.8% interest compounded daily, and is held for 5 years. Assume 360 days in a year. (Round your answer to the nearest cent.)
P = Po(1+r)^n.
Po = $27,000.
r = (5.8%/360) / 100% = 0.00016111 =
Daily % rate expressed as a decimal.
n = 360Comp./yr * 5yrs=1800 Compounding
periods.
Plug the above values into the given Eq
and solve for P.
P = $36,082.70.
Int. = P - Po
9082.70
To find the amount of compound interest earned, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount after interest has been compounded
P = the principal (initial amount)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal (P) is $27,000, the annual interest rate (r) is 5.8% (or 0.058 as a decimal), the interest is compounded daily (n = 365), and we're holding the account for 5 years (t = 5).
Plugging in the values into the formula:
A = 27000(1 + 0.058/365)^(365 * 5)
Now, we can calculate this using a calculator or a computer program. After evaluating the expression, we find that the final amount (A) is approximately $34,223.41.
To find the compound interest earned, we subtract the principal from the final amount:
Compound interest = A - P
= $34,223.41 - $27,000
= $7,223.41
Therefore, the amount of compound interest earned in this account is approximately $7,223.41.