Question

Look for 1145 = tijzot too

Need help solving this.

This is a formula of Yield to Maturity. I already know how to solve it using excel but I need to know how it can be solved manually (thru calculator).

Thanks

Answer 1

1) if you have financial calculator, then

Inputs: present value (pv) = -1,145

Future value (Fv) = 1,000

Coupon (pmt) = 40

Time (n) ,= 20

Ytm = Compute

We get, Ytm = 3.023%

You can cross check by putting the value of i as 3.023% in the equation.

2) if you are using different calculator then you can try trial and error method.

For trial and error the interest rate should be less than coupon rate because the present value is more than future value and this can only happen if interest rate is less than coupon rate.

If we choose interest rate as 3%, then

Putting the value in equation LHS = RHS , if this doesn't happen then answer is not correct.

1,145 = 40/i {1-1/(1+i)^20} + 1,000/(1+i)^20

1,145 = 40/0.03 { 1-1/(1+0.03)^20} + 1,000/(1+0.03)^20

1,145 = 1,333.33 { 1-1/(1.03)^20} + 1,000/(1.03)^20

1,145 = 1,333.33 {1-1/1.8061} + 1,000/1.8061

1,145 = 1,333.33 {1-0.5537} + 553.68

1,145 = 1,333.33 (0.4463) + 553.68

1,145 = 595.07 + 553.68

1,145 = 1,148.75

As we can see that there is a minor difference between LHS and RHS, so the interest rate needs to be a bit higher and not much.

3) We can also use interpolation to get ytm.

As we have calculated for 3% , we need to calculate the same way for 4%. Then interpolate the value of two to get the ytm.