Question

Find the effective rate of the compound interest rate or investment. (Round your answer to two decimal places.) A $50,000 zero-coupon bond maturing in 8 years and selling now for $43,035. %

Answer 1

Ans. Effective annual rate=1.8928%

Annual Compound semi-annually=1.8839%

Explanation:

Hi, this is the formula to find the effective annual rate for this zero-coupon bond.

`EffectiveAnnualRate=\sqrt[n]{(FaceValue)/(Price) } -1`

n= years to maturity

That is:

`EffectiveAnnualRate=\sqrt[8]{(50,000)/(43,035) } -1=0.018928`

Means that the effective interest rate is 1.8928% effective annual

Now, let´s find the compound interest rate.

First, we have to turn this rate effective semi-annually

`Semi-AnnualRate=(1+0.018928)^{(1)/(2) }  -1=0.00942`

0.942% effective semi annual

To turn this into a semi-annual, compounded semi-annually, we just have to multiply by 2, so we get.

1.8839% compounded semi-annually

Best of luck