With an applicable annual interest rate of 7%, what is the required annual payment into an investment account to have $90,000 in the investment account in ten years starting from $0 in the investment account?

Question

BlackTom AI · Accepted Answer

We’re given an annual interest rate of 7% and a target future value of $90,000 after 10 years starting with $0. We need to determine the annual payment to contribute each year.

Option 1: $5,714.88. To check this, recall the formula for the future value of an ordinary annuity (payments at end of each year): FV = PMT * [((1 + r)^n − 1) / r]. Solving for PMT gives PMT = FV * r / ((1 + r)^n − 1). If we plug r = 0.07, n = 10, and FV = 90,000, we get PMT ≈ 90,000 * 0.07 / ((1.07)^10 − 1). Using (1.07)^10 ≈ 1.96715, the denominator ≈ 0.96715, so PMT ≈ 6,300 / 0.96715 ≈ 6,510 to 6,515. This value is somewhat close but slightly lower than many precise calculations, and 5,714.88 is notably below the computed range, suggesting it’s too small to reach 90,000 in 10 years.

Option 2: $6,513.98. This aligns well with the standard calculation: PMT = 90,000 * 0.07 / ((1.07)^10 − 1). Using (1.07)^10 ≈ 1.96715, the denominator is about 0.96715, giving PMT ≈ 6,300 / 0.96715 ≈ 6,513.98. This matches the mathematical solution for an ordinary annuity with end-of-year payments and 7% annual interest, so it is a correct result under the ordinary annuity assumption.

Option 3: $7,316.49. This amount is noticeably larger than the standard ordinary annuity calculation with 7% interest over 10 years. If we test it in the same formula, the resulting FV would exceed $90,000, meaning this payment would produce more than the target, so this option is too high for the given parameters.

Option 4: $4,619.26. This value is clearly smaller than the required payment to reach $90,000 in 10 years at 7% interest. Using the formula in reverse, this payment would accumulate to well under $90,000, indicating this option is insufficient to achieve the goal within the specified period.

In summary, among the given choices, the amount that matches the standard calculation for an ordinary annuity with a 7% return over 10 years to reach $90,000 is approximately $6,513.98, while the other options fall short or exceed what’s needed for the target with the stated assumptions.

With an applicable annual interest rate of 7%, what is the required annual payment into an investment account to have $90,000 in the investment account in ten years starting from $0 in the investment account?单项选择题

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