Final answer:
By applying the compound interest formula, the future value of a $5,900 deposit compounded daily at 7.5% interest over 4 years is approximately $8,145.90.
Step-by-step explanation:
To calculate the future value of an investment with compound interest, we use the formula A = P(1 + r/n)^(n*t), 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 or borrowed for, in years.
In this case, we're given:
- P = $5,900
- r = 7.5% or 0.075
- n = 365 (since the interest is compounded daily)
- t = 4 years
Inserting these values into the formula, we get:
A = $5,900(1 + 0.075/365)^(365*4)
The calculation will provide us with the final amount. Always remember to convert percentages to decimal form by dividing by 100 before calculations.
Upon calculation, the final value comes to:
A = $5,900(1 + 0.00020547945)^(1460) =$8,145.90