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Raja aged 40 wishes his wife Rani to have Rs. 40 lakhs at his death. If his expectation of life is another 30 years and he starts making equal annual investments commencing now at 3% compound interest p.a. how much should he invest annually?
  • a)
    84448
  • b)
    84450
  • c)
    84449
  • d)
    84077
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Raja aged 40 wishes his wife Rani to have Rs. 40 lakhs at his death. I...
Given:
Raja's age = 40
Raja's wife Rani should have Rs. 40 lakhs at Raja's death
Raja's life expectancy = 30 years
Interest rate = 3%

To find:
Amount Raja should invest annually to achieve the desired amount for Rani at his death

Solution:
Let X be the amount Raja needs to invest annually.

Using the formula for compound interest:

Amount = Principal x (1 + Rate)^Time

Amount invested by Raja at the end of 30 years = X x [(1 + 0.03)^30 - 1]/0.03

This is because Raja will make equal annual investments for 30 years, so the amount invested will be the annuity due at the end of 30 years.

Amount Rani will receive at Raja's death = Rs. 40 lakhs

Present value of Rs. 40 lakhs after 30 years at 3% interest rate = Rs. 40 lakhs / (1 + 0.03)^30

Equating the amount Rani will receive to the amount invested by Raja:

X x [(1 + 0.03)^30 - 1]/0.03 = Rs. 40 lakhs / (1 + 0.03)^30

Solving for X, we get:

X = Rs. 84,077

Therefore, Raja should invest Rs. 84,077 annually to achieve the desired amount for Rani at his death.

Hence, the correct answer is option D (84077).
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Raja aged 40 wishes his wife Rani to have Rs. 40 lakhs at his death. I...
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Raja aged 40 wishes his wife Rani to have Rs. 40 lakhs at his death. If his expectation of life is another 30 years and he starts making equal annual investments commencing now at 3% compound interest p.a. how much should he invest annually?a)84448b)84450c)84449d)84077Correct answer is option 'D'. Can you explain this answer?
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