Independent solution

How to solve this Loan Amortization question

Setup

Setup

Express each level payment as interest on the prior balance plus the observed principal reduction.

m=125000i+250=124750i+252m=125000i+250=124750i+252

Model

Model

Equating the two payment expressions determines the monthly rate, after which either expression gives the payment.

i=2250=0.008,m=1250i=\frac{2}{250}=0.008,\qquad m=1250

Compute

Compute

Value the remaining level-payment stream at loan issue and solve the annuity factor for n.

125000=1250an‾∣ 0.008⟹(1.008)−n=0.2125000=1250a_{\overline{n}|\,0.008}\Longrightarrow(1.008)^{-n}=0.2

Answer

Answer

The real-valued term rounds to about 202 monthly payments, so choice E is correct.

n=202 payments(E)\boxed{n=202\text{ payments}\quad\text{(E)}}

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; 0.8 I/Y; 125000 PV; 1250 +/- PMT; 0 FV; CPT NN = 201.98END mode; I/Y is the monthly effective rate. A final payment makes the count 202.