Final answer:
The value of a $3,000 savings account with 3% interest compounded daily after five years is approximately $3,477.82.
Step-by-step explanation:
To find the value of a $3,000 savings account that pays 3% interest compounded daily after five years, we can 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 for, in years.
Given:
- P = $3,000
- r = 3% or 0.03
- n = 365 (since the interest is compounded daily)
- t = 5 years
Plugging in these values:
A = $3,000(1 + 0.03/365)365*5
Calculating this gives us:
A ≈ $3,000(1 + 0.00008219178082)1825
A ≈ $3,000 * 1.1592740741
A ≈ $3,477.82
The savings account will be worth approximately $3,477.82 after five years.