Interpolating to find interest rates - where do you start?

[Paapi]

Hi everyone,


So i noticed that there is a lot of interpolating to do to find a specific interest rate in almost all the past papers. However my question is how do you figure out which particular rate to try first?

For e.g
77.7378 = 5 a^(2)_20 + 100 V^20

in this example the examiners report have first tried i = 8%

How do you know that you should first try 8%???

 

[Polz87]

Theres a clever way to come up with a starting guess for interpolation that is found in the ASET solutions:

the coupons of 5 a year after paying an initial 77.7378 gives a return of 5/77.7378 = 0.0643 = 6.43% per year.

Considering the redemption payment of 100, this is a gain of
100 - 77.7378 = 22.2622. As a percentage this is 22.2622/77/7378 = 0.2864 = 28.64%. Spread over the 20 years , this is an average of 28.64/20 = 1.43% per year.

So an initial guess for the overall return is the total of the return from coupons and the return from the capital gain 6.43+1.43= 7.86.

Since the capital payment is actually all at the end and not spread over the 20 years, and this is the bit which gets discounted the most, the actual rate of return must be higher so 8% is a good first guess.

 

[Mark Mitchell]

You might reason approximately as follows:

You pay 78, and receive 5 per year for 20 years. So this is like a return of 5/78 = 6.4% per year.

But on top of that you get more back at the end (100) than you paid (78). Like making a capital gain. You gain 100 -78 = 22 over 20 years. This is like getting an additional return of about 1 per year. So, in % terms this is an additional return of 1/78 = 1.3% per year.

Overall an approximate rate of 6.4% + 1.3% = 7.7%.

Then round to the nearest integer.

Note that you don't score marks for your first guess - it just saves you time on the trial and improvement to find the correct answer. The alternative to working out a first guess is to just pick something and go with it!