Independent solution

How to solve this Loan Amortization question

Setup

Setup

At the fifth payment date, value the original 20 remaining scheduled payments immediately before applying the extra principal payment.

B5−=1300a20‾∣ 0.07=13772.20B_5^-=1300a_{\overline{20}|\,0.07}=13772.20

Model

Model

Subtract the additional 2,600 from that balance; the result is refinanced over the desired 15-year horizon.

B5+=13772.20−2600=11172.20B_5^+=13772.20-2600=11172.20

Compute

Compute

Dividing the reduced balance by the 15-year annuity factor at 7% gives 1,226.65.

P=B5+/a15‾∣ 0.07=1226.65P=B_5^+/a_{\overline{15}|\,0.07}=1226.65

Answer

Answer

The revised annual payment is 1,226.65, corresponding to choice B.

P=1226.65(B)\boxed{P=1226.65\quad\text{(B)}}

Calculator reproduction

BA II Plus keystrokes

Check END/BGN, period, sign, TVM, and cash-flow setup

  1. 2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 20 N; 7 I/Y; 1300 +/- PMT; 0 FV; CPT PVPV = 13772.22END mode; I/Y is annual. This is the balance immediately before the extra principal payment.
  2. 2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 15 N; 7 I/Y; 11172.22 PV; 0 FV; CPT PMTPMT = -1226.65END mode; I/Y is annual. The reduced balance is positive and the rescheduled payments are negative.