If you purchased a 1,000 Goldman Sachs (GS) 10 year coupon...

If you purchased a $1,000 Goldman Sachs (GS) 10 year coupon bond, today, with a coupon rate of a 5.5 percent, the coupon payment would be $ 55. (Enter your response as an integer.) Then, tomorrow, interest rates rose to 6.0 percent, the price of the bond would fall to $ 917. (Enter your response as an integer.) Hence, there is a(n) inverse relationship between interest rates and the price of the bond.

Transcript

00:01 Hello everyone.

00:02 We are given the following information.

00:04 We have bond j and bond k.

00:06 The coupon rate, year of maturity, power value, ymt are given to us.

00:11 We are asked when their interest rate rises by 3 % what is the percentage change in the bond? first of all, we need to calculate a present value.

00:20 Then when the increase rate by 3 % what happens? and then we have to find the percentage change.

00:27 So first of all, the coupon rate.

00:28 So how do we find the coupon rate? we have to multiply the par value with the coupon rate.

00:36 So this is going to be 0 .055 and this is going to be 0 .155.

00:43 So the coupon payment will be power value into the coupon rate.

00:47 So that is going to be 0 .055 and the value is 55 and since the rate is given in dollars, we have thousand dollars here.

00:58 So this will be in dollars.

01:00 This is going to be $1 ,000.

01:03 Thousand into 0 .155, which is equal to $1505.

01:11 So what happens when the rate increases by 3 %? so before going to that, we need to find the present value.

01:26 Present value and the formula is equal to fv, future value 1 divided by 1 plus r to the power n.

01:36 Or we can use the excel where the function, we have to go in the finesse.

01:41 Financial column and we have to choose the function pv and we just need to substitute the value and we will be getting the present value.

01:48 So what is that is pv of the rate? the rate given to us is 6%.

01:57 So how do we find this as 6 % is? since they pay semi -annual payment, that is we are given that semi -annual payment, we need to convert the given data to semi.

02:13 So therefore we will have for bond j and bond j we'll be getting we have 55 right so 55 divided by 2 which is equal to 27 .5 dollars and this side we'll be getting 155 divided by 2 which is going to be 77 .5.

02:53 This is the coupon payment.

02:56 Now next is next we have this the year of maturity we have to multiply this by 2 so 8 into 2 will be giving 16 here it's also 8 so 8 2 will be equal to 16 next is ym t y t m so this will be 12 % right so 12 % divided by 2 which is going to be 6 % and this will also be 6 % now that we have found for semi -payment we need to substitute the values so we know that pv is given by the formula pv 6 % 16 the year of maturity comma the value and this rate so this will be noted by p .0 so therefore p .0 will be equal to 671 .55 so now that we have calculate the present value so let's highlight that we need to calculate p1 so how do we we find p1 that is after the increase right so we'll be getting 3 % interest rate implies new ytm will be equal to 12 plus 3 that is going to be 15 % now the coupon amount is nothing but for semi this is for semi 27 .5 dollars and we know that the year of maturity is going to be 16...

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