Final answer:
To calculate the future value of $3,250 with daily compound interest at an annual rate of 4.75% over 4 years, the compound interest formula is used. The values are substituted into the formula A = P(1 + r/n)^(nt) to compute the final amount in the account after the given period.
Step-by-step explanation:
The question involves calculating the future value of an investment with daily compound interest. To determine the amount in the account after 4 years, 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 or borrowed for, in years.
In this case, P is $3,250, r is 4.75% or 0.0475 in decimal form, n is 365 (since the interest is compounded daily), and t is 4 years. Substituting these values into the formula, we get:
A = 3250(1 + 0.0475/365)^(365*4)
Using a calculator, we compute the value of A to reach the final amount.