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

1. 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%