Very simple rate combination

Question

If I borrow £150 in total - £100 at 5% and £50 at 10%, what is the combined rate of my loan?

If my instincts are correct, the combined rate should be 6.25%?

I'm just trying to model this in software and I wanted to confirm.

Thanks and apologies for the simpleness of this questionner.

Answer 1

Let's see:

A first loan of £100 at 5% = £105 at end of period n.

A second loan of £50 at 10% = £55 at end of period n.

Total loans is £150 at x% = £160 at end of period n.

$x=(160/150)-1$

$x=(16/15)-1$

$x=1/15$

Answer 2

Too many people are unaware of the harmonic mean

The harmonic mean is the answer to all questions regarding an average of the rate / velocity / speed.

In your case, the answer is $$\frac{50+100}{\frac{50}{1.10}+\frac{100}{1.05}}=1.066$$

So your average interest rate is 6.6%