Independent solution

How to solve this Loan Balances Between Payment Dates question

Setup

Setup

Compute the scheduled annual payment using the 10% effective annual loan rate.

P=10000a10‾∣0.10=1627.45P=\frac{10000}{a_{\overline{10}|0.10}}=1627.45

Model

Model

Immediately after the third payment, seven payments remain. The prospective balance is their value at time 3.

B3=1627.45a7‾∣0.10B_3=1627.45a_{\overline{7}|0.10}

Compute

Compute

The time-3 balance is 7,923.13. During the next half-year the contract applies simple interest, so multiply by 1 plus 0.10 times 0.5.

B3=7923.13B_3=7923.13
B3.5=7923.13(1+0.10(0.5))=8319.28B_{3.5}=7923.13(1+0.10(0.5))=8319.28

Answer

Answer

The halfway balance rounds to 8,319, which is choice E.

B3.5≈8319(E)\boxed{B_{3.5}\approx8319\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2ND · CLR TVMTVM worksheet clearedUse END mode and P/Y = C/Y = 1.
  2. 10 · NN = 10
  3. 10 · I/YI/Y = 10
  4. 10000 · PVPV = 10,000
  5. 0 · FVFV = 0
  6. CPT · PMTPMT = -1,627.45
  7. 7 · N · CPT · PVPV = 7,923.13This is the balance immediately after payment 3.