Independent solution

How to solve this Interest Rate Valuation question

Setup

Setup

Convert the annual effective discount rate directly to its one-year present-value factor.

v=1−d=1−0.032=0.968v=1-d=1-0.032=0.968

Model

Model

The withdrawals occur at years two through twelve, while the remaining balance is also valued at year twelve.

50000=X∑k=16v2k+45000v1250000=X\sum_{k=1}^{6}v^{2k}+45000v^{12}

Compute

Compute

Discount every outflow to the deposit date and equate their total to the initial deposit.

50000=X∑k=16(0.968)2k+45000(0.968)1250000=X\sum_{k=1}^{6}(0.968)^{2k}+45000(0.968)^{12}

Answer

Answer

This timing and discount convention match choice C.

equation in choice C\boxed{\text{equation in choice C}}