Independent solution

How to solve this Loan Amortization question

Setup

Setup

Recover the original loan amount from the scheduled sixty-payment annuity.

im=0.03/12=0.0025,L=359.37a60‾∣ im=20000i_m=0.03/12=0.0025,\qquad L=359.37a_{\overline{60}|\,i_m}=20000

Model

Model

Use a retrospective balance at month 36 and add back the accumulated values of the two payments that were not made.

B36=L(1+im)36−359.37s36‾∣ im+359.37(1+im)11+359.37(1+im)10B_{36}=L(1+i_m)^{36}-359.37s_{\overline{36}|\,i_m}+359.37(1+i_m)^{11}+359.37(1+i_m)^{10}

Compute

Compute

The resulting balance immediately after the month-36 payment is 9,099.17.

B36=9099.17B_{36}=9099.17

Answer

Answer

The closest listed balance is 9,099, corresponding to choice E.

B36≈9099(E)\boxed{B_{36}\approx9099\quad\text{(E)}}