Equations of Value and Time Diagram

Problem 12.1 In return for payments of $5,000 at the end of 3 years and$4,000 at the end of 9 years, an investor agrees to pay $1500 immediately and to make an additional payment at the end of 2 years. Find the amount of the additional payment if i^{(4)} = 0.08. Solution. 5,000(1 + \frac{0.08}{4})^{-3 \times 4} + 4,000(1 + \frac{0.08}{4})^{-9 \times 4} \\ = 1,500 + X(1 + \frac{0.08}{4})^{-2...

Solving for Unknown Time

Problem 14.1 The present value of a payment of $5,000 to be made in t years is equal to the present value of a payment of$7,100 to be made in 2t years. If i = 7.5\% find $t4. Solution. 5,000(1+0.075)^{-t} = 7,100(1+0.075)^{-2t} \\ \implies 5,000 = 7,100(1 + 0.075)^{-t} \\ \implies t = 4.84...

Solving for the Unknown Interest Rate

Problem 12.1 In return for payments of $5,000 at the end of 3 years and$4,000 at the end of 9 years, an investor agrees to pay $1500 immediately and to make an additional payment at the end of 2 years. Find the amount of the additional payment if i^{(4)} = 0.08. Solution. 5,000(1 + \frac{0.08}{4})^{-3 \times 4} + 4,000(1 + \frac{0.08}{4})^{-9 \times 4} \\ = 1,500 + X(1 + \frac{0.08}{4})^{-2...