You have just started a new job and plan to save $4,650 per year for 43 years until you retire. You will make your first deposit in one year. How much will you have when you retire if you earn an annual interest rate of 10.31 percent?

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BlackTom AI · Accepted Answer

We start by restating the scenario: you contribute a fixed amount each year (an ordinary annuity) of 4,650 dollars for 43 years, with the first deposit made one year from now, and the account earns 10.31% interest annually. The question asks for the future value at retirement.
Option A: $3,021,337.12. This value aligns with the ordinary annuity future value formula FV = PMT * [((1 + r)^n - 1) / r], using PMT = 4,650, r = 0.1031, n = 43. With a precise calculation, (1.1031)^43 is a large growth factor, subtracting 1 and dividing by r yields a multiplier in the neighborhood of ~646, and multiplying by 4,650 yields just over 3.0 million, which matches this option.
Option B: $2,878,036.49. This is a plausible but smaller result, suggesting either a lower compounding effect or a slightly smaller multiplier. It would occur if the growth factor or the annuity multiplier were underestimated (for example, not accounting for the full (1+r)^n term). However, the given inputs should produce a higher value than this if computed accurately.
Option C: $2,734,735.86. This is noticeably lower, implying a substantial underestimation of the compound growth or an error such as using a smaller n, a misapplied formula, or treating deposits as occurring at the beginning of periods (which would actually increase the value). In short, this value reflects too little accumulation for the given terms.
Option D: $2,889,974.64. This sits between the underestimates and the correct ballpark but still falls short of the precise ordinary annuity FV with the specified r and n. It could arise from rounding intermediate steps or using a slightly different rate or timing assumption, but it does not match the exact calculation.
Option E: $2,917,153.08. Similar to Option D, this is an approximate figure that’s not exact. It suggests a minor miscalculation in the exponent or the divisor, but again it’s not the precise ordinary annuity future value with the stated inputs.
In evaluating these options, the key points are to apply the correct formula for an ordinary annuity (deposits at the end of each period, first deposit one year from now), use the exact interest rate 10.31% per year, and multiply the resulting annuity factor by the annual payment 4,650. Deviations from this approach (e.g., using an annuity due, miscounting the number of periods, or rounding too aggressively) lead to values seen in the incorrect choices.
So, after comparing all options and recalling the standard FV of an ordinary annuity formula, the most precise match to the computation is Option A: $3,021,337.12.

You have just started a new job and plan to save $4,650 per year for 43 years until you retire. You will make your first deposit in one year. How much will you have when you retire if you earn an annual interest rate of 10.31 percent?

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