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%
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