Independent solution

How to solve this Interest Earned During a Period question

Setup

Setup

For a level-rate account, interest earned in a given year equals the balance at the start of that year times i. Write both stated interest amounts in that form.

100(1+i)10i=50(1+i)16i100(1+i)^{10}i=50(1+i)^{16}i

Model

Model

Cancel the common rate factor. The equality then reduces to (1 + i)⁶ = 2, which determines the effective annual rate.

(1+i)6=2⟹i=21/6−1=0.122462(1+i)^6=2\Longrightarrow i=2^{1/6}-1=0.122462

Compute

Compute

Using i = 2 to the power 1/6 − 1 in the first account’s year-11 interest expression gives 38.879, or 38.90.

X=100(1+i)10i=38.879X=100(1+i)^{10}i=38.879

Answer

Answer

The calculation gives 38.90 for interest earned during a period, matching published choice E.

X=38.90(E)\boxed{X=38.90\quad\text{(E)}}