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.