Independent solution

How to solve this Loan Balances and Amortization question

Setup

Setup

Equate the present values of the two level-payment loans.

Pak‾∣i=120a5k‾∣jPa_{\overline{k}|i}=120a_{\overline{5k}|j}

Model

Model

The rate relation makes the discount factors after k grouped periods identical, so the annuity numerators cancel.

1+i=(1+j)51+i=(1+j)^5
a5k‾∣jak‾∣i=ij\frac{a_{\overline{5k}|j}}{a_{\overline{k}|i}}=\frac{i}{j}

Compute

Compute

Thus P is 120 times the fifth-power rate increment divided by j. Over the stated interval its limiting bounds are 600 and 649.96.

P=120(1+j)5−1jP=120\frac{(1+j)^5-1}{j}
600<P<649.958707600<P<649.958707

Answer

Answer

The payment lies between 600 and 650, which is choice E.

600<P≤650(E)\boxed{600<P\le650\quad\text{(E)}}