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Suppose the U.S. Treasury offers to sell you a bond for $3,000. No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $5,000. What interest rate would you earn if you bought this bond at the offer price? (Hint: Be careful about the sign of cash flows because this problem is to solve for the interest rate.)

a. 3.82%
b. 4.25%
c. 4.72%
d. 5.24%
e. 5.77%

Respuesta :

Answer:

d. 5.24%

Explanation:

firstly we are given the present value of the bond which is $3000 which is Pv.

then they further give us the the future value of the bond which is $5000  which is Fv, furthermore we are also given the period of the bond that it will mature by which is in 10 years which will be n. we are now told to calculate the interest rate i for this bond to mature to $5000; so we will use the future value formula which is :

[tex]Fv =Pv (1+i)^n[/tex]

now we substitute the values and solve for i the interest rate.

  $5000= $3000(1+i)^10 then we divide by $3000 both sides,

$5000/$3000 = (1+i)^10 then we find the 10nth root of both sides

,[tex]\sqrt[10]{5/3}[/tex] =1+i then we subtract both sides by 1 to solve for i

0.05240977915 = i then we multiply by 100 as this is an interest rate.

therefore i the interest rate is 5.24% then we round off to two decimal places.

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