Two bonds are available on the market as follows: Bond 1: Face value $250, 5 years to maturity at a (simple) interest rate of 5%. Bond 2: F

Question

Two bonds are available on the market as follows: Bond 1: Face value $250, 5 years to maturity at a (simple) interest rate of 5%. Bond 2: Face value $350, 3 years to maturity at a (simple) interest rate of r. Given that both bonds yield the same interest to maturity, calculate r.

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Anna 6 days 2021-10-13T05:24:24+00:00 1 Answer 0

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    2021-10-13T05:25:58+00:00

    The value of r is 5.95%

    Step-by-step explanation:

    The formula of the simple interest is I = P r t, where

    • P is the initial amount of money
    • r is the interest rate in decimal
    • t is the time

    Bond 1:

    ∵ The face value is $250

    ∴ P = 250

    ∵ The value is in the bond for 5 years

    ∴ t = 5

    ∵ The simple interest rate is 5%

    ∴ r = 5% = 5 ÷ 100 = 0.05

    ∵ I = P r t

    – Substitute the values of P, r and t in the rule

    ∴ I = (250)(0.05)(5) = 62.5

    The interest of Bond 1 is $62.5

    Bond 2:

    ∵ The face value is $350

    ∴ P = 350

    ∵ The value is in the bond for 3 years

    ∴ t = 3

    ∵ The simple interest rate is r

    ∵ I = P r t

    – Substitute the values of P and t in the rule

    ∴ I = (350)(r)(3) = 1050 r

    The interest of Bond 2 is 1050 r

    ∵ The both bonds yield the same interest to maturity

    – Equate the interests of bonds 1 and 2

    ∵ 1050 r = 62.5

    – Divide both sides by 1050

    r = 0.0595

    – Multiply it by 100% to change it to percentage

    ∵ r = 0.0595 × 100% = 5.95%

    ∴ r = 5.95%

    The value of r is 5.95%

    Learn more:

    You can learn more about interest in brainly.com/question/11149751

    #LearnwithBrainly

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