# Very simple rate combination [closed]

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.

• So are you borrowing £(150+100)=£250 at 5%? Feb 27, 2016 at 16:00
• No, sorry £150 in total. Feb 27, 2016 at 16:01
• @UriGoren - I upvoted both answers already. Have marked one as answer now Mar 23, 2016 at 9:17

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.

$x=(160/150)-1$

$x=(16/15)-1$

$x=1/15$

• This is the method I ended up using as it was easier for a maths noob like me to understand. Thanks. Mar 23, 2016 at 9:16

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%

• Thanks for your answer - it helped me a lot. Mar 23, 2016 at 9:15