Answer:
$67,377.37.
Step-by-step explanation:
Certainly! Here's how to find the compound interest and final amount for a principal of $55,000 invested for 3 years at 7% annual interest compounded annually:
Formula:
The most common formula for compound interest (CI) is:
CI = P * (1 + r/n)^(n*t)
where:
CI - Compound Interest (amount of interest earned on the interest)
P - Principal amount (initial investment) - $55,000 in this case
r - Annual interest rate (as a decimal) - 7% which is equal to 0.07
n - Number of times interest is compounded per year (in this case, annually so n = 1)
t - Number of years
Calculation:
Plug in the values:
CI = 55,000 * (1 + 0.07 / 1)^(1 * 3)
Simplify the expression:
CI = 55,000 * (1.07) ^ 3
Calculate using a calculator:
CI ≈ $12,377.37 (round to the cent)
Final Amount:
The final amount (F) can be found by adding the compound interest (CI) to the initial principal amount (P).
F = P + CI
F = 55,000 + 12,377.37
F ≈ $67,377.37 (round to the cent)
Interpretation:
The compound interest earned over 3 years is approximately $12,377.37.
The final amount after 3 years, considering the compounded interest, is approximately $67,377.37.
Note:
This calculation assumes annual compounding. If the interest were compounded more frequently (e.g., semi-annually, quarterly, monthly), the compound interest earned would be slightly higher due to the "interest on interest" effect accumulating more often.
