Independent solution

How to solve this Loan Balances and Amortization question

Setup

Setup

Use the 2% quarterly rate to compute the balance after the first twenty payments.

B20=100000(1.02)20−2500s20‾∣0.02B_{20}=100000(1.02)^{20}-2500s_{\overline{20}|0.02}

Model

Model

Solve the exact level-payment term at 5,000; because a balloon is required, take 21 full payments and a larger final payment.

B20=5000am‾∣0.02B_{20}=5000a_{\overline m|0.02}
m=21.86311892m=21.86311892

Compute

Compute

After 21 full payments the remaining balance before the next due date is 4236.70. Accumulating once and adding the regular 5,000 gives 9321.43.

Bballoon=5000+4236.69559058(1.02)=9321.42950239B_{\mathrm{balloon}}=5000+4236.69559058(1.02)=9321.42950239

Answer

Answer

The final balloon payment is approximately 9,237, selecting choice E.

B≈9237(E)\boxed{B\approx9237\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2ND · CLR TVM · 20 · N · 2 · I/Y · 100000 · +/- · PV · 2500 · PMT · CPT · FVFV = 87851.32Use signs consistently; the magnitude is the remaining balance.
  2. 2 · I/Y · 87851.32 · +/- · PV · 5000 · PMT · 0 · FV · CPT · NN = 21.86