The annual coupon rate is 2%, but coupons are paid semiannually. The yield to maturity was 1.85%. If the par value is $100,000, how much did you pay for this bond

Hi the number of years to maturity  for this Bond is missing. I have tried to search for the  full question online but could not find it. However, I will help you get the technique to solve this problem.

The amount of money you pay for the Bond is its Present Value (PV) normally called Current Price of the Bond.

To calculate this, you should have the other remaining elements of the Bond which are : Coupon rate (PMT) , Period of payments within a year (P/YR), Yield To Maturity (YTM), Par Value (Future Value of Bond).

So assuming that the Bond in question matures in 5 years the calculation will be as follows :

Pmt = (1,000,000 × 2%) ÷ 2 = $10,000

Ytm = 1.85 %

Fv = $1,000,000

P/yr = 2

N = 5 × 2 = 10

Pv = ?

You would pay $1,007,132 for this bond

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