Independent solution

How to solve this Loan Amortization question

Setup

Setup

Use a prospective balance immediately after the twelfth scheduled payment.

B12=1000a24‾∣ 0.0075=21889.15B_{12}=1000a_{\overline{24}|\,0.0075}=21889.15

Model

Model

Equate that balance to the present value of the increased monthly payments.

21889.15=2000an‾∣ 0.007521889.15=2000a_{\overline{n}|\,0.0075}

Compute

Compute

The level-payment term is 11.46 months, meaning eleven full payments cannot quite retire the debt.

n=11.46n=11.46

Answer

Answer

A final drop payment is therefore made in the twelfth month after the change, choice C.

payoff occurs in month 12(C)\boxed{\text{payoff occurs in month }12\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 24 N; 0.75 I/Y; 0 FV; 1000 +/- PMT; CPT PVPV = 21889.15
  2. 21889.15 PV; 2000 +/- PMT; 0 FV; CPT NN = 11.46Eleven full payments are followed by a month-12 drop payment.