Final answer:
Jeff's ending balance after one year on his $2,300 deposit with 3.13% interest compounded weekly is approximately $2,375.01. The closest answer choice to the calculated value is C) $2,375.39, which is the correct option.
Step-by-step explanation:
To calculate Jeff's ending balance after one year with an initial deposit of $2,300 at an interest rate of 3.13% compounded weekly, we will use the formula for compound interest:
A = P × (1 + r/n)^(nt)
- P is the principal amount ($2,300)
- r is the annual interest rate (3.13% or 0.0313)
- n is the number of times interest is compounded per year (52 weeks)
- t is the number of years the money is invested (1 year)
Substituting the values into the formula:
A = $2,300 × (1 + 0.0313/52)^(52×1)
After calculating the above expression, we find:
A = $2,300 × (1 + 0.0006019)^52
A = $2,300 × (1.0006019)^52
A = $2,300 × 1.032178387 ≈ $2,375.01
Therefore, the correct ending balance after one year is approximately $2,375.01. The closest option to our calculation is C) $2,375.39, so we can conclude that this is the correct answer even though there is a slight rounding difference.