Independent solution

How to solve this Loan Amortization question

Setup

Setup

Interest in a payment equals the rate times the balance immediately before that payment.

I11=1200−300v10−900v20I_{11}=1200-300v^{10}-900v^{20}

Model

Model

Use prospective balances after payments 10 and 20 to express both interest portions through v to the tenth power.

I21=900(1−v10)I_{21}=900(1-v^{10})

Compute

Compute

The stated two-to-one relation reduces to a quadratic, whose positive-rate root is v to the tenth equal to two-thirds.

I11=2I21⟹9v20−15v10+6=0,v10=2/3I_{11}=2I_{21}\Longrightarrow9v^{20}-15v^{10}+6=0,\quad v^{10}=2/3

Answer

Answer

The twenty-first payment's interest is therefore 300, corresponding to choice C.

I21=900(1−2/3)=300(C)\boxed{I_{21}=900(1-2/3)=300\quad\text{(C)}}