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10,000 can be invested under two options: Option 1. Deposit the 10,000 into a fund earning an effective annual rate of i; or Option 2. Purchase an annuity-immediate with 24 level annual payments at an effective annual rate of 10%. The payments are deposited into a fund earning an effective annual rate of 5%. Both options produce the same accumulated value at the end of 24 years. Calculate i.

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ogorwyne

Answer:

I = 0.06894

Explanation:

The investment amount into 2 options is given as 10000

10000x(1+I)²⁴ is the accumulated value of option a

10000x0.10/(1-i)/1.1²⁴/0.05x1.05^24-1

= 49530.62522

To get I

(49530.62522/10000)^1/24-1

= 1.068995077 - 1

= 0.06894

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