Your great aunt Matilda put some money in an account for you on the day you were born. This account pays 8% interest per year. On your 21st birthday the account balance was $5033.83.

The amount of money that your great aunt Matilda originally put in the account is closest to:

Question

Your great aunt Matilda put some money in an account for you on the day you were born. This account pays 8% interest per year. On your 21st birthday the account balance was $5033.83.

The amount of money that your great aunt Matilda originally put in the account is closest to:

BlackTom AI · Accepted Answer

We start by identifying the relationship between the present value (initial deposit P), the annual interest rate r = 8%, and the amount after t = 21 years. With annual compounding, the future value A after t years is A = P × (1 + r)^t. Here A is given as 5033.83 and r = 0.08, t = 21.

Step 1: Compute the accumulation factor (1 + r)^t = 1.08^21. A quick approximation uses natural logs or iterative multiplication. A commonly used estimate is 1.08^21 ≈ 5.03. (This matches the idea that 8% growth for 21 years roughly multiplies the original amount by about five.)

Step 2: Solve for the initial amount P. From A = P × (1.08)^21, we get P = A / (1.08^21).
Using the approximation: P ≈ 5033.83 ÷ 5.03 ≈ 1000.0.

Step 3: Check each answer option by back-calculating the final amount using the same accumulation factor (approximately 5.03).
- If P = $600: final ≈ 600 × 5.03 ≈ 3018. ≈ $3,018, which is far from $5,033.83.
- If P = $800: final ≈ 800 × 5.03 ≈ 4,024, which is still short of $5,033.83.
- If P = $1000: final ≈ 1000 × 5.03 ≈ 5,030, which is very close to $5,033.83.
- If P = $1200: final ≈ 1200 × 5.03 ≈ 6,036, which is higher than the given amount.

Step 4: Compare the closeness of each option. The calculated final amount for $1000 aligns most closely with 5033.83, whereas the other options yield totals that are noticeably farther away when using the same accumulation factor.

Step 5: Reflect on potential rounding. Small differences can arise from the exact value of 1.08^21; even with a more precise factor, the $1000 choice remains the closest initial deposit because it produces a final amount that matches the given balance most closely.

Corporate Finance Homework 1

Your great aunt Matilda put some money in an account for you on the day you were born. This account pays 8% interest per year. On your 21st birthday the account balance was $5033.83. The amount of money that your great aunt Matilda originally put in the account is closest to:

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