compound interest earned in an account that opens with $28,000, earns 2.4% interest compounded daily, and is held for 10 years. Assume 360 days in a year
P = Po(1+r)^n.
P = Principal after 10 years.
Po = $28,000 = Inital deposit.
r = (2.4%)/360) / 100% = 0.00006667. =
Daily % rate expressed as a decimal.
n = 360Comp/yr * 10yrs=3600 Compounding periods.
Plug the above values into the given Eq
and get:
P = $35,594.69.
I = P-Po =
To calculate the compound interest earned in the given account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the final amount (including both the principal and interest)
P = the principal amount (initial deposit)
r = annual interest rate (expressed as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, we have:
P = $28,000
r = 2.4% = 0.024 (expressed as a decimal)
n = 360 (since interest is compounded daily)
t = 10 years
Plugging these values into the formula, we get:
A = 28000(1 + 0.024/360)^(360*10)
Now, let's calculate it step by step to get the compound interest earned:
Step 1: Calculate the inside parentheses:
(1 + 0.024/360) = 1.00006667
Step 2: Raise the inside result to the power of the number of compound periods:
1.00006667^(360*10) ≈ 1.259712979
Step 3: Multiply the principal amount by the result from Step 2:
28000 * 1.259712979 ≈ $35,233.19
Hence, the compound interest earned in the account is approximately $35,233.19.