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 would be in the account if you left the money there until your 65th birthday 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 would be in the account if you left the money there until your 65th birthday is closest to:

BlackTom AI · Accepted Answer

To approach this problem, we start by understanding the compounding process: the amount recorded at age 21 is the initial principal grown for 21 years at 8% annually. Then we project that same balance forward to age 65 using the same rate.

Option-by-option examination:

Option A: $29,556
- This value is far too small to be the balance at age 65 given the 21-year balance is $5,033.83. If the balance can reach over $5,000 in 21 years, growing only to about $29k by age 65 would require much less than 44 years of compounding, which is inconsistent with 44 years at 8%. Therefore this is not plausible.

Option B: $148,780
- A direct way to check is to see what the 21st birthday amount would grow to by age 65: multiply 5033.83 by (1.08)^(65−21) = (1.08)^44. Using common exponent approximations, (1.08)^44 is about 29.6. Then 5033.83 × 29.6 ≈ 149,000. This falls very close to $148,780, making this option plausible and consistent with standard compound growth.

Option C: $168,824
- While this is in the same general magnitude, it would require (1.08)^44 to be about 33.5 since 5033.83 × 33.5 ≈ 168,000. However, (1.08)^44 is closer to 29.6 based on standard growth tables or calculator results. This makes $168,824 somewhat too large given 44 years at 8% and the actual 21-year balance. Thus this is less consistent with the calculation.

Option D: $748,932
- This would imply an enormous growth factor far beyond (1.08)^44. It would require roughly 149 times growth from 5033.83, which contradicts the 8% yearly rate over 44 years. Such a result ignores the steady compounding provided and is not feasible with the given data.

Summary of reasoning:
- The correct approach uses a forward-compounding factor (1.08)^44 applied to the 21st-birthday balance of $5,033.83.
- The computed product is near $148,780, aligning with option B.
- The other options diverge either by underestimating (A) or overestimating (C and D) the growth expected from 44 years at 8%.

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 would be in the account if you left the money there until your 65th birthday is closest to:

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