Independent solution

How to solve this Loan Refinancing question

Setup

Setup

Immediately after the fifth scheduled payment, 20 original payments remain.

B5=1300a20‾∣0.08B_5=1300a_{\overline{20}|0.08}

Model

Model

The extra 4,000 reduces this balance. The remainder is repaid by ten new level payments X.

1300a20‾∣0.08−4000=Xa10‾∣0.081300a_{\overline{20}|0.08}-4000=Xa_{\overline{10}|0.08}

Compute

Compute

The post-extra-payment balance is 8,763.59 and the ten-year annuity factor is 6.710081.

B5−4000=8763.59B_5-4000=8763.59
X=8763.59/6.710081=1306.03X=8763.59/6.710081=1306.03

Answer

Answer

The revised annual payment rounds to 1,306, which is choice C.

X≈1306(C)\boxed{X\approx1306\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2ND · CLR TVMTVM worksheet clearedUse END mode and annual periods.
  2. 20 · NN = 20
  3. 8 · I/YI/Y = 8
  4. 1300 · +/- · PMTPMT = -1,300
  5. 0 · FV · CPT · PVPV = 12,763.59
  6. − 4000 =8,763.59Balance after the extra payment.
  7. 10 · N · 8763.59 · PV · 0 · FV · CPT · PMTPMT = -1,306.03