Two investment options are as follows. Choice 1: Payments of $ 2550 now, $ 3100 a year from now, and $ 3720 two years from now.

Question

Two investment options are as follows. Choice 1: Payments of $ 2550 now, $ 3100 a year from now, and $ 3720 two years from now.

Choice 2: Three yearly payments of $ 3100 starting now.
Assume interest is compounded continuously.
What is the interest rate that would make both choices equally lucrative?

Answer 1

The present value of Choice 1 is 2550 + 3100e^(-r) + 3720e^(-2r). The present value of Choice 2 is 3100 + 3100e^(-r) + 3100e^(-2r). Setting the two equations equal to each other and solving for r yields an interest rate of approximately 0.068.

Answer 2

Two investment options are as follows. Choice 1: Payments of $ 2550 now, $ 3100 a year from now, and $ 3720 two years from now.

The present value of Choice 1 is 2550 + 3100e^(-r) + 3720e^(-2r). The present value of Choice 2 is 3100 + 3100e^(-r) + 3100e^(-2r). Setting the two equations equal to each other and solving for r yields an interest rate of approximately 0.068.

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