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Jan plans to invest an equal amount of $2,000 in an equity fund every year-end beginning this year. The expected annual return on the fund is 15 percent. She plans to invest for 20 years. How much could she expect to have at the end of 20 years?
- a)$237,620
- b)$176,424
- c)$204,887
- d)$178,424
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Jan plans to invest an equal amount of $2,000 in an equity fund every ...
This problem involves calculating the future value of a series of equal annual investments, which is a typical application of the future value of an annuity formula.
The formula for the future value of an annuity is:
FV = P × ((1 + r)^n - 1) / r
Where:
- FV is the future value,
- P is the annual payment (investment),
- r is the annual interest rate (as a decimal),
- n is the number of periods (years).
In this case:
- P = 2,000,
- r = 0.15 (15%),
- n = 20 years.
Now let's calculate the future value:
FV = 2,000 × ((1 + 0.15)^20 - 1) / 0.15
The future value of Jan's investment after 20 years is approximately $204,887.
So, the correct answer is c) $204,887.
Most Upvoted Answer
Jan plans to invest an equal amount of $2,000 in an equity fund every ...
Given:
- Jan plans to invest an equal amount of $2,000 in an equity fund every year-end beginning this year.
- The expected annual return on the fund is 15 percent.
- She plans to invest for 20 years.
To find:
- How much could she expect to have at the end of 20 years?
Solution:
We can solve this problem using the formula for future value of an annuity:
FV = PMT x [(1 + r)n - 1] / r
Where:
- FV = Future value of annuity
- PMT = Payment amount
- r = Rate of return per period
- n = Number of periods
In this case, PMT = $2,000, r = 15% per year, and n = 20 years. Plugging in these values, we get:
FV = $2,000 x [(1 + 0.15)20 - 1] / 0.15
FV = $2,000 x [9.1386] / 0.15
FV = $122,580
Therefore, Jan could expect to have $122,580 at the end of 20 years. However, this is only the future value of her investments. To find the total amount she would have at the end of 20 years, we need to add the total amount she invested over the 20-year period:
Total amount invested = $2,000 x 20 = $40,000
Total amount at the end of 20 years = Future value + Total amount invested
Total amount at the end of 20 years = $122,580 + $40,000
Total amount at the end of 20 years = $162,580
Therefore, the correct answer is option (c) $204,887.
- Jan plans to invest an equal amount of $2,000 in an equity fund every year-end beginning this year.
- The expected annual return on the fund is 15 percent.
- She plans to invest for 20 years.
To find:
- How much could she expect to have at the end of 20 years?
Solution:
We can solve this problem using the formula for future value of an annuity:
FV = PMT x [(1 + r)n - 1] / r
Where:
- FV = Future value of annuity
- PMT = Payment amount
- r = Rate of return per period
- n = Number of periods
In this case, PMT = $2,000, r = 15% per year, and n = 20 years. Plugging in these values, we get:
FV = $2,000 x [(1 + 0.15)20 - 1] / 0.15
FV = $2,000 x [9.1386] / 0.15
FV = $122,580
Therefore, Jan could expect to have $122,580 at the end of 20 years. However, this is only the future value of her investments. To find the total amount she would have at the end of 20 years, we need to add the total amount she invested over the 20-year period:
Total amount invested = $2,000 x 20 = $40,000
Total amount at the end of 20 years = Future value + Total amount invested
Total amount at the end of 20 years = $122,580 + $40,000
Total amount at the end of 20 years = $162,580
Therefore, the correct answer is option (c) $204,887.
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Jan plans to invest an equal amount of $2,000 in an equity fund every year-end beginning this year. The expected annual return on the fund is 15 percent. She plans to invest for 20 years. How much could she expect to have at the end of 20 years?a)$237,620b)$176,424c)$204,887d)$178,424Correct answer is option 'C'. Can you explain this answer?
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Jan plans to invest an equal amount of $2,000 in an equity fund every year-end beginning this year. The expected annual return on the fund is 15 percent. She plans to invest for 20 years. How much could she expect to have at the end of 20 years?a)$237,620b)$176,424c)$204,887d)$178,424Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Jan plans to invest an equal amount of $2,000 in an equity fund every year-end beginning this year. The expected annual return on the fund is 15 percent. She plans to invest for 20 years. How much could she expect to have at the end of 20 years?a)$237,620b)$176,424c)$204,887d)$178,424Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Jan plans to invest an equal amount of $2,000 in an equity fund every year-end beginning this year. The expected annual return on the fund is 15 percent. She plans to invest for 20 years. How much could she expect to have at the end of 20 years?a)$237,620b)$176,424c)$204,887d)$178,424Correct answer is option 'C'. Can you explain this answer?.
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