Question

Spartan Credit Bank is offering 7.5 percent compounded daily on its savings accounts. You deposit $5,900 today.

a. How much will you have in the account in 4 years? (Use 365 days a year. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

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