Question

Alan has $100 in a savings account that earns 10% interest per year. The interest is not compounded. How much interest will he earn in 4 years?

a) $10
b) $20
c) $30
d) $40

Answer 1

The simple interest is calculated by multiplying the principal amount ($100) by the interest rate (10%) and the time (4 years). So, $100 * 10% * 4 = $40. Alan will earn $40 in interest after 4 years, option (d).

Explanation:

Alan's interest earnings can be determined using the simple interest formula:
`\(I = P * R * T\)`, where (I) is the interest, (P) is the principal amount, (R) is the interest rate, and (T) is the time. In this scenario, Alan has $100
`(\(P\))` in a savings account with a 10% ((R)) annual interest rate. After 4 years
`(\(T\))`, the calculation becomes
`\(I = 100 * 0.10 * 4\)`, resulting in $40 in interest.

This amount is earned linearly, without compounding, as the interest is based solely on the initial principal. Each year, Alan accumulates $10 in interest
`(\(100 * 0.10\))`, and over the 4-year period, this sums to a total interest of $40.

Understanding simple interest is crucial for financial planning, especially when dealing with straightforward interest calculations. It provides a clear method for determining how much interest accrues over time based on an initial amount and a fixed interest rate. In this case, the simplicity of the interest calculation makes it easy to grasp that Alan will earn $40 in interest over the 4-year period.