# Weighted Average Rate with multiple variables

## Easy - Situation 1.

I have an existing loan with $$\200\;000$$ balance and a $$4.00\%$$ interest rate. I take out an additional $$\200\;000$$ loan on the same property and current rates are at $$8.00\%$$. The lender blends the rates to $$6.00\%$$.

## My limit - Situation 2.

If my existing loan only has $$3$$ years remaining and the new $$\400,000$$ loan is going to be on a $$5$$-year term, they would give a lower weighting to the existing loan's lower amount. (Please forgive my weak formatting, I had to lookup guides to complete the equation below.) $$0.04\cdot\frac{3}{3+5}+0.08 \cdot\frac{5}{3+5} = 0.065$$

## My question - Situation 3.

How would I calculate taking into account both the remaining term, and the balances, if they were different? If my existing loan was only $$\100\;000$$ at $$4.00\%$$ with $$3$$ years remaining, and I was taking out another $$\200\;000$$ at $$8.00\%$$. With the new $$\300\;000$$ loan over $$5$$ years, how do I calculate the blended rate? My equations below seems broken and I am not sure why. $$0.04\cdot\frac 3{3+5}\cdot\frac {100\;000}{100\;000+200\;000)}+0.08 \cdot\frac 5{3+5}\cdot\frac {200\;000}{100\;000+200\;000} = 0.0383$$

Is it because I need to add another $$0.04$$ multiplier, add them together and divide by two? I feel like I am close, but something just is not clicking. (Also, I am struggling with formatting that.)
$$\frac{0.04\cdot\frac{3}{3+5}+0.04\cdot\frac{1}{(1+2)}+0.08\cdot\frac {5}{3+5}+0.08\cdot\frac{2}{1+2}}{2} = \frac{0.1317}{2} = 0.065833$$

I think I accidentally worked my way into the answer, but I do not understand.

I am also trying to do this the simple way of giving equal weighting to both variables. If the variables were not equally weighted, I do not think simply dividing by $$2$$ would fix.