Final Answer:
The balance after 14 years, with daily compounding interest, will be approximately $20,518.16.
Step-by-step explanation:
For compound interest, the formula to calculate the future value of an investment is given by the compound interest formula: A = P(1 + r/n)^(nt), where:
- A is the future value of the investment/loan, including interest.
- P is the principal investment amount ($7500 in this case).
- r is the annual interest rate (7.1% in decimal form is 0.071).
- n is the number of times that interest is compounded per year (daily compounding means n = 365, as there are 365 days in a year).
- t is the time the money is invested for in years (14 years).
Using this formula, substitute the given values to find the future balance after 14 years:
A = 7500 * (1 + 0.071/365)^(365*14)
By solving this equation, you'd arrive at the final balance after 14 years, which would be approximately $20,518.16.
Daily compounding interest allows for more frequent accrual of interest on the initial principal as well as on the accumulated interest. As a result, the investment grows substantially over time compared to simple or less frequent compounding periods. In this case, the initial deposit of $7500 grows to over $20,000 due to the effect of daily compounding, showcasing the power of compounding over an extended period at a decent interest rate.