Final answer:
The balance in Pennywise's savings account after 3 years with an interest rate of 1.5% compounded daily would be calculated using the compound interest formula. Compound interest adds interest to the principal sum as well as to the accumulated interest from previous periods. This differentiates it from simple interest, which only applies to the principal amount.
Step-by-step explanation:
To find the balance in Pennywise's savings account after 3 years with an interest rate of 1.5% compounded daily, you would use the compound interest formula. This is because compound interest involves calculating the interest on both the principal and the accumulated interest over previous periods. In this scenario, the formula needed is:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount ($3,000 in this case).
- 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.
Let's walk through an example:
Suppose you deposit $100 into a bank account with a 2% annual interest rate, compounded annually. After one year, the balance would be $102. The following year, it's 1.02 times $102, resulting in $104.04. After three years, using the pattern revealed, the amount would be $106.18, which is $100 times (1.02)^3.
Comparatively, using simple interest, the total future amount for a $100 deposit at a 5% interest rate held for three years would be:
Total future amount (with simple interest) = $100 + ($100 × 0.05 × 3) = $115
This shows a direct line of interest without compounding, contrasting with compound interest, which includes interest on previously accumulated interest.