Independent solution

How to solve this Loan Balances and Amortization question

Setup

Setup

Compute the contractual 40-quarter payment at 2% per quarter and apply the first rounding rule.

X=5000000a40‾∣0.02X=\frac{5000000}{a_{\overline{40}|0.02}}
R1=183000R_1=183000

Model

Model

Find the balance after twenty rounded payments, then apply the second rounding rule.

B20=5000000(1.02)20−183000s20‾∣0.02B_{20}=5000000(1.02)^{20}-183000s_{\overline{20}|0.02}
R2=200000R_2=200000

Compute

Compute

The second-stage exact term is 17.891297, so it uses 18 payments including the drop.

B20=200000an‾∣0.02B_{20}=200000a_{\overline n|0.02}
N=20+⌈17.89129668⌉=38N=20+\lceil17.89129668\rceil=38

Answer

Answer

The loan requires 38 total payments, selecting choice C.

N=38(C)\boxed{N=38\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2ND · CLR TVM · 40 · N · 2 · I/Y · 5000000 · +/- · PV · 0 · FV · CPT · PMTPMT = 182778.74
  2. 20 · N · 5000000 · +/- · PV · 183000 · PMT · CPT · FVFV = 2983318.31
  3. 2983318.31 · +/- · PV · 200000 · PMT · 0 · FV · CPT · NN = 17.89Round up to include the drop payment.