Because each $630 deposit is made at the start of the month, the cash-flow pattern is an annuity due. There will be 36 deposits over three years. The future-value relationship is:
$25,000 = $630 × [((1 + r)³⁶ − 1) ÷ r] × (1 + r)
Solving for the monthly return produces approximately 0.52% per month . The nominal annualised rate is approximately:
0.52% × 12 = 6.24%
The corresponding effective annual return is approximately 6.42%. Both calculations are closest to 6% , making option C correct.
Without investment growth, the client would contribute only:
$630 × 36 = $22,680
The investment therefore needs to generate approximately $2,320 of additional value. Because deposits occur at the beginning rather than the end of each month, every contribution earns one additional month of return compared with an ordinary annuity. Treating the deposits as year-end or month-end payments would produce an inaccurate required rate.
The Retail Securities syllabus specifically requires the application of time-value-of-money calculations to determine the regular investment needed to meet a known future financial objective or liability.
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