Final answer:
To calculate the interest earned from a $14,000 deposit at 5% APR compounded weekly over eight years, use the compound interest formula to find the total amount and then subtract the principal. The interest earned, rounded to the nearest cent, is approximately $6,723.36.
Step-by-step explanation:
To calculate the interest earned when $14,000 is deposited for eight years at a 5% APR with compounding weekly interest, we use the compound interest formula:
A = P(1 + r/n)(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
For our calculation:
- P = $14,000
- r = 5% or 0.05 (as a decimal)
- n = 52 (because interest is compounded weekly)
- t = 8 years
Using the formula:
A = 14000(1 + 0.05/52)(52*8)
We calculate A, and then to find the interest earned, subtract the principal (P) from the amount (A):
Interest Earned = A - P
Calculating A:
A = 14000(1 + 0.05/52)(52*8)
A ≈ 14000(1 + 0.000961538)416
A ≈ 14000 * 1.48024
A ≈ $20,723.36
Therefore, the interest earned is approximately:
Interest Earned = $20,723.36 - $14,000
Interest Earned ≈ $6,723.36
To the nearest cent, the interest earned is $6,723.36.