Travis International has a debt payment of $2.33 million that it must make 5 years from today. The company does not want to come up with the entire amount at that time, so it plans to make equal monthly deposits into an account starting 1 month from now to fund this liability. If the company can earn a return of 5.28 percent compounded monthly, how much must it deposit each month?

Question

BlackTom AI · Accepted Answer

We start by identifying the cash flow details and the time/value framework. The liability is 2.33 million to be paid in 5 years, and Travis International plans to fund it with equal monthly deposits starting one month from now, with a nominal annual return of 5.28% compounded monthly. This means the monthly interest rate i is 0.0528/12 = 0.0044 (or 0.44%). The number of deposits is n = 5 years × 12 months/year = 60 deposits.

Option A: 34,943.29
This value would imply a monthly payment somewhat larger than the calculated figure. If we compute the future value of an ordinary annuity with PMT around this amount using i = 0.0044 and n = 60, the resulting accumulated value would exceed 2.33 million. Therefore this option is too high given the target liability and the low monthly rate.

Option B: 38,833.33
This amount is quite large for the given interest rate and horizon. In fact, it would produce a substantially higher accumulated sum than 2.33 million after 60 months. The calculation PMT = FV × i / [(1+i)^n − 1] shows that a payment this large would overshoot the target, making this choice inconsistent with the required funding.

Option C: 36,285.33
Again, this payment is larger than the amount needed to reach 2.33 million under the stated rate. Plugging into the standard future-value annuity formula would yield a final value well above the target, indicating overfunding relative to the liability.

Option D: 34,017.49
This aligns with the standard formula for the future value of an ordinary annuity. Using i = 0.0044 and n = 60, the required monthly payment PMT is PMT = FV × i / [(1+i)^n − 1]. Substituting FV = 2,330,000, i = 0.0044, and (1+i)^n ≈ (1.0044)^60 ≈ 1.3012 gives PMT ≈ 2,330,000 × 0.0044 / (1.3012 − 1) ≈ 2,330,000 × 0.0044 / 0.3012 ≈ 34,000. The more precise calculation yields about 34,017.49, which matches this option.

To summarize the reasoning for each option, consider the core relationship: the required monthly payment is the size that, when compounded monthly at 0.44% for 60 months, grows to 2.33 million. Options that are larger than this target will overfund, while smaller options underfund the obligation. The computation using the standard future-value of an ordinary annuity confirms that the appropriate payment is approximately 34,017.49.

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