Roger has just lost a lawsuit and has agreed to make equal annual payments of $15,500 for the next 7 years with the first payment due today. The value of this liability today is $88,000. What is the interest rate on the payments

7.615%

Explanation:

we can use the present value of an annuity formula to determine the interest rate:

present value of an annuity due = (payment / i) x (1 + i) x {1 - [1 / (1 + i)ⁿ]}

80,000 = (15,500/ i) x (1 + i) x {1 - [1 / (1 + i)⁷]}

1 - [1 / (1 + i)⁷] = 80,000 / [(15,500/ i) x (1 + i)]

1 - 80,000 / [(15,500/ i) x (1 + i)] = 1 / (1 + i)⁷

(1 + i)⁷ = 1 / {1 - 80,000 / [(15,500/ i) x (1 + i)]}

(1 + i)⁷ = 1 / {[(15,500/ i) x (1 + i) - 80,000] / [(15,500/ i) x (1 + i)]}

1 + i = ⁷√(1 / {[(15,500/ i) x (1 + i) - 80,000] / [(15,500/ i) x (1 + i)]})

1 + i = ⁷√(1 / {[1/i - 64,500] / [(15,500/ i + 15,500)]})

...

after a lot of complicated math,

1 + i = 1.07615

i = 0.07615 = 7.615%

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