Independent solution

How to solve this Two-Phase Loan Amortization question

Setup

Setup

During the first ten years, each payment equals 150% of that year’s interest. Thus interest is paid in full and an additional 5% of the opening balance is retired each year.

B10=1000(1−0.05)10=598.74B_{10}=1000(1-0.05)^{10}=598.74

Model

Model

The first phase therefore leaves 1,000(0.95)¹⁰ = 598.74. The second phase is a ten-payment level amortization at 10%, so that balance must equal X times the ten-year annuity-immediate factor.

B10=Xa10‾∣ 0.10B_{10}=Xa_{\overline{10}|\,0.10}

Compute

Compute

Dividing 598.74 by the annuity factor gives X = 97.44. The requested whole-unit payment is 97.

X=598.74/a10‾∣ 0.10=97.44X=598.74/a_{\overline{10}|\,0.10}=97.44

Answer

Answer

The calculation gives 97 for two-phase loan amortization, matching published choice D.

X=97(D)\boxed{X=97\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 10 N; 10 I/Y; 598.74 +/- PV; 0 FV; CPT PMT97.44Use END mode and annual periods for the second amortization phase.