weighted average of interest rate
$begingroup$
Let say that I have 2 loans. One loan has an interest rate of 5% and the other of 10%. I calculate the weighted average both loans and it is 8% (This is an example). I don't know how can you prove that the total interest yield of both loans with thier original interest rates is the same as if both loans interest rate was 8%. I don't know how to prove it. I would like some intuition.
average
asked Sep 25 '18 at 23:23
kprincipekprincipe
998
$endgroup$
add a comment |
$begingroup$
Let say that I have 2 loans. One loan has an interest rate of 5% and the other of 10%. I calculate the weighted average both loans and it is 8% (This is an example). I don't know how can you prove that the total interest yield of both loans with thier original interest rates is the same as if both loans interest rate was 8%. I don't know how to prove it. I would like some intuition.
average
asked Sep 25 '18 at 23:23
kprincipekprincipe
998
$endgroup$
$begingroup$
How do you calculate that the "weighted average of both loans" is 8^%? The only way I know to find such a weighted average is use the fact that "the total interest yield of both loans with their original interest rates is the same as if both loans interest rate was 8%." You don't need to prove it- that is the definition of "weighted average".
$endgroup$
– user247327
Sep 25 '18 at 23:30
$begingroup$
my confusion is for example, let say that loan 1 is a loan with a term of 60 month at 5% and that at the end the loan will yield 2000 in interest. Also Loan 2 is with term of 60 month at 7% and the loan will yield 2500. The balance of the loan does not matter my confusion y how can i be sure that using the weight average will yiled the same 4500 in interest. you know that the interest of a loan is not just multiplying the balance by the rate, there is an amortization process
$endgroup$
– kprincipe
Sep 26 '18 at 0:22
add a comment |
$begingroup$
Let say that I have 2 loans. One loan has an interest rate of 5% and the other of 10%. I calculate the weighted average both loans and it is 8% (This is an example). I don't know how can you prove that the total interest yield of both loans with thier original interest rates is the same as if both loans interest rate was 8%. I don't know how to prove it. I would like some intuition.
average
asked Sep 25 '18 at 23:23
kprincipekprincipe
998
$endgroup$
Let say that I have 2 loans. One loan has an interest rate of 5% and the other of 10%. I calculate the weighted average both loans and it is 8% (This is an example). I don't know how can you prove that the total interest yield of both loans with thier original interest rates is the same as if both loans interest rate was 8%. I don't know how to prove it. I would like some intuition.
average
average
asked Sep 25 '18 at 23:23
kprincipekprincipe
998
asked Sep 25 '18 at 23:23
kprincipekprincipe
998
asked Sep 25 '18 at 23:23
kprincipekprincipe
998
asked Sep 25 '18 at 23:23
kprincipekprincipe
998
asked Sep 25 '18 at 23:23
kprincipekprincipe
998
998
$begingroup$
How do you calculate that the "weighted average of both loans" is 8^%? The only way I know to find such a weighted average is use the fact that "the total interest yield of both loans with their original interest rates is the same as if both loans interest rate was 8%." You don't need to prove it- that is the definition of "weighted average".
$endgroup$
– user247327
Sep 25 '18 at 23:30
$begingroup$
my confusion is for example, let say that loan 1 is a loan with a term of 60 month at 5% and that at the end the loan will yield 2000 in interest. Also Loan 2 is with term of 60 month at 7% and the loan will yield 2500. The balance of the loan does not matter my confusion y how can i be sure that using the weight average will yiled the same 4500 in interest. you know that the interest of a loan is not just multiplying the balance by the rate, there is an amortization process
$endgroup$
– kprincipe
Sep 26 '18 at 0:22
add a comment |
$begingroup$
How do you calculate that the "weighted average of both loans" is 8^%? The only way I know to find such a weighted average is use the fact that "the total interest yield of both loans with their original interest rates is the same as if both loans interest rate was 8%." You don't need to prove it- that is the definition of "weighted average".
$endgroup$
– user247327
Sep 25 '18 at 23:30
$begingroup$
my confusion is for example, let say that loan 1 is a loan with a term of 60 month at 5% and that at the end the loan will yield 2000 in interest. Also Loan 2 is with term of 60 month at 7% and the loan will yield 2500. The balance of the loan does not matter my confusion y how can i be sure that using the weight average will yiled the same 4500 in interest. you know that the interest of a loan is not just multiplying the balance by the rate, there is an amortization process
$endgroup$
– kprincipe
Sep 26 '18 at 0:22
$begingroup$
How do you calculate that the "weighted average of both loans" is 8^%? The only way I know to find such a weighted average is use the fact that "the total interest yield of both loans with their original interest rates is the same as if both loans interest rate was 8%." You don't need to prove it- that is the definition of "weighted average".
$endgroup$
– user247327
Sep 25 '18 at 23:30
$begingroup$
How do you calculate that the "weighted average of both loans" is 8^%? The only way I know to find such a weighted average is use the fact that "the total interest yield of both loans with their original interest rates is the same as if both loans interest rate was 8%." You don't need to prove it- that is the definition of "weighted average".
$endgroup$
– user247327
Sep 25 '18 at 23:30
$begingroup$
my confusion is for example, let say that loan 1 is a loan with a term of 60 month at 5% and that at the end the loan will yield 2000 in interest. Also Loan 2 is with term of 60 month at 7% and the loan will yield 2500. The balance of the loan does not matter my confusion y how can i be sure that using the weight average will yiled the same 4500 in interest. you know that the interest of a loan is not just multiplying the balance by the rate, there is an amortization process
$endgroup$
– kprincipe
Sep 26 '18 at 0:22
$begingroup$
my confusion is for example, let say that loan 1 is a loan with a term of 60 month at 5% and that at the end the loan will yield 2000 in interest. Also Loan 2 is with term of 60 month at 7% and the loan will yield 2500. The balance of the loan does not matter my confusion y how can i be sure that using the weight average will yiled the same 4500 in interest. you know that the interest of a loan is not just multiplying the balance by the rate, there is an amortization process
$endgroup$
– kprincipe
Sep 26 '18 at 0:22
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Set the interests equal to each other to figure the relative size of the loans.
$.08x + .08y = .05x + .10y$
$.03x = .02y$
$x = frac{2}{3}y$
Therefore the $x$ loan is $frac{2}{3}$ of the $y$ loan.
Example:
$x = 600; y = 900$
$.08x + .08y = .05x + .10y$
$.08(600) + .08(900) = .05(600) + .10(900)$
$48 + 72 = 30 + 90$
$120 = 120$
answered Sep 25 '18 at 23:37
Phil HPhil H
4,2882312
$endgroup$
add a comment |
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1 Answer
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1 Answer
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votes
$begingroup$
Set the interests equal to each other to figure the relative size of the loans.
$.08x + .08y = .05x + .10y$
$.03x = .02y$
$x = frac{2}{3}y$
Therefore the $x$ loan is $frac{2}{3}$ of the $y$ loan.
Example:
$x = 600; y = 900$
$.08x + .08y = .05x + .10y$
$.08(600) + .08(900) = .05(600) + .10(900)$
$48 + 72 = 30 + 90$
$120 = 120$
answered Sep 25 '18 at 23:37
Phil HPhil H
4,2882312
$endgroup$
add a comment |
$begingroup$
Set the interests equal to each other to figure the relative size of the loans.
$.08x + .08y = .05x + .10y$
$.03x = .02y$
$x = frac{2}{3}y$
Therefore the $x$ loan is $frac{2}{3}$ of the $y$ loan.
Example:
$x = 600; y = 900$
$.08x + .08y = .05x + .10y$
$.08(600) + .08(900) = .05(600) + .10(900)$
$48 + 72 = 30 + 90$
$120 = 120$
answered Sep 25 '18 at 23:37
Phil HPhil H
4,2882312
$endgroup$
add a comment |
$begingroup$
Set the interests equal to each other to figure the relative size of the loans.
$.08x + .08y = .05x + .10y$
$.03x = .02y$
$x = frac{2}{3}y$
Therefore the $x$ loan is $frac{2}{3}$ of the $y$ loan.
Example:
$x = 600; y = 900$
$.08x + .08y = .05x + .10y$
$.08(600) + .08(900) = .05(600) + .10(900)$
$48 + 72 = 30 + 90$
$120 = 120$
answered Sep 25 '18 at 23:37
Phil HPhil H
4,2882312
$endgroup$
Set the interests equal to each other to figure the relative size of the loans.
$.08x + .08y = .05x + .10y$
$.03x = .02y$
$x = frac{2}{3}y$
Therefore the $x$ loan is $frac{2}{3}$ of the $y$ loan.
Example:
$x = 600; y = 900$
$.08x + .08y = .05x + .10y$
$.08(600) + .08(900) = .05(600) + .10(900)$
$48 + 72 = 30 + 90$
$120 = 120$
answered Sep 25 '18 at 23:37
Phil HPhil H
4,2882312
answered Sep 25 '18 at 23:37
Phil HPhil H
4,2882312
answered Sep 25 '18 at 23:37
Phil HPhil H
4,2882312
answered Sep 25 '18 at 23:37
Phil HPhil H
4,2882312
4,2882312
add a comment |
add a comment |
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$begingroup$
How do you calculate that the "weighted average of both loans" is 8^%? The only way I know to find such a weighted average is use the fact that "the total interest yield of both loans with their original interest rates is the same as if both loans interest rate was 8%." You don't need to prove it- that is the definition of "weighted average".
$endgroup$
– user247327
Sep 25 '18 at 23:30
$begingroup$
my confusion is for example, let say that loan 1 is a loan with a term of 60 month at 5% and that at the end the loan will yield 2000 in interest. Also Loan 2 is with term of 60 month at 7% and the loan will yield 2500. The balance of the loan does not matter my confusion y how can i be sure that using the weight average will yiled the same 4500 in interest. you know that the interest of a loan is not just multiplying the balance by the rate, there is an amortization process
$endgroup$
– kprincipe
Sep 26 '18 at 0:22