Final answer:
To calculate the future value of an investment compounded daily at a 4% annual interest rate over 25 years, the formula A = P(1 + r/n)^nt is used. With an initial deposit of $18,000, the future value is approximately $49,806.09.
Step-by-step explanation:
To calculate the future value of an investment with compound interest, we use the 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.
In this case, a couple deposits $18,000 into an account earning 4% annual interest, compounded daily for 25 years. The daily compounding means that the interest is compounded 365 times a year (n = 365).
Let's convert the annual interest rate from a percentage to a decimal by dividing by 100: r = 4/100 = 0.04. Now, we can plug in the values into the formula:
A = 18000(1 + 0.04/365)365 * 25
Now that we have the formula set up, we can calculate the value:
A = 18000(1 + 0.000109589)9125
Calculating the expression inside the parentheses first and then using exponentiation, we can find the future value A.
By doing the math, we find that the future value of the investment, A, is approximately $49,806.09 after 25 years of daily compounding.