Which interest rate is the better?

[Rosedala]

Hello, I know the following is awfully simple if one understands numbers...I'm embarrassed but I must know:

Which is a better rate:

3 years at 2.50%

OR:

2 years at 2.22% ?

Thanks ever so much!

 

[Deleted member 4993]

Hello, I know the following is awfully simple if one understands numbers...I'm embarrassed but I must know:

Which is a better rate:

3 years at 2.50%

OR:

2 years at 2.22% ?

Thanks ever so much!

What do you mean by better rate?

However, this problem is pretty clear - 2.5% (assuming APR) return is higher than 2.22% APR (irrespective of number of years).

 

[JeffM]

Hello, I know the following is awfully simple if one understands numbers...I'm embarrassed but I must know:

Which is a better rate:

3 years at 2.50%

OR:

2 years at 2.22% ?

Thanks ever so much!

2.50% APR is a HIGHER rate than 2.22% APR. PERIOD.

Whether that makes it a BETTER rate is a different issue. What is the probability that you will need the money in fewer than 3 years. This is called liquidity risk. If there is virtually no risk that you will need the money in under 3 years, how do you evaluate the prospects for interest rates in 2 years. If you expect that, 2 years from now, the rate for 1 year will be at 10% and you are correct, it will be MORE PROFITABLE to invest for 2 years now at 2.22% and 1 year at 10% in 2 years than to invest now for 3 years at 2.5%. If, however, you expect that, in two years, the rate for 1 year will be 1% and you are correct, it will be MORE PROFITABLE to invest now for 3 years at 2.5%. This is called reinvestment or market risk.

Your question is far from simple because you are comparing two things that differ in two different respects, rate and term. It's why bond traders die young.

 

[Denis]

Depends on "expected" 3rd year rate; break even if 3.06% :

2.5% : 1.025^3 = 1.077
2.22%: 1.022^2 = 1.045 ; 1.045 * 1.0306 = 1.077

 

[JeffM]

Depends on "expected" 3rd year rate; break even if 3.06% :

2.5% : 1.025^3 = 1.077
2.22%: 1.022^2 = 1.045 ; 1.045 * 1.0306 = 1.077

This is exactly true only if the probability is exactly zero that you will need your money in sooner than 3 years. But it is an excellent approximation if that probability is very low. Of course that still does not determine which investment is BETTER because you need to know the probabilities on what the 1 year rate will be in 2 years.

As I said, this is a very difficult problem that almost certainly does not have a universally CORRECT answer. Suppose you like the taste of hamburgers better than the taste of hot dogs, but hot dogs are cheaper. Hampurgers are tastier, but hot dogs are cheaper so different people will decide differenly about which is better.