Multiple Loan Interest Cost Optimization

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Beast869

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Joined
Jun 27, 2023
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I have 2 loans of various interest rates, balances, and minimum payments.

Assuming I have a certain amount of money to pay out each month, how can I minimize the total amount I pay over the lifetime of the loans?

Given:
Total Monthly payment: M
Interest Rate for each loan: R1, R2
Initial Principal for each Loan: P1, P2
Minimum Monthly Payment: Min1, Min2

Assumptions:
I must pay at least the minimum payment on each loan each month. For each month I need to make 2 payments, one for each loan.
I can pay more than the minimum amount.

Here are some fictional values to get started:

Loan 1:
P1 = $45,000
R1 = 4%
Min1 = $1,000/Month

Loan 2:
P2 = $20,000
R2 = 5.5%
Min2 = $250/Month

M = $3,000

In the scenario above I would need $1,250 to make the minimum payment on each of the loans. How should I use the remaining $1,750 each month to overpay some of the loans, so that I minimize the amount of money I pay over the lifetime of the loans? (Assume payments are made once per month.)

Ultimately, I want to know how should I distribute M over the 4 loans each month. Does anyone have a formula that can be used to approach this problem?
 
Ultimately, I want to know how should I distribute M over the 4 loans each month. Do you mean 2 loans and not 4 loans?
Shouldn't you pay the extra money to the higher interest loan?

Asking for a formula is not how you do math. You think, think again and then decide on a method to use.

What have you recently learned in class. Can you use calculus, etc?
 
Did you try breaking up the 1750 into Q1 + Q2 and see how that works out?
 
Beast869 said:
I have 2 loans of various interest rates, balances, and minimum payments.

Assuming I have a certain amount of money to pay out each month, how can I minimize the total amount I pay over the lifetime of the loans?

Given:
Total Monthly payment: M
Interest Rate for each loan: R1, R2
Initial Principal for each Loan: P1, P2
Minimum Monthly Payment: Min1, Min2

Assumptions:
I must pay at least the minimum payment on each loan each month. For each month I need to make 2 payments, one for each loan.
I can pay more than the minimum amount.

Here are some fictional values to get started:

Loan 1:
P1 = $45,000
R1 = 4%
Min1 = $1,000/Month

Loan 2:
P2 = $20,000
R2 = 5.5%
Min2 = $250/Month

M = $3,000

In the scenario above I would need $1,250 to make the minimum payment on each of the loans. How should I use the remaining $1,750 each month to overpay some of the loans, so that I minimize the amount of money I pay over the lifetime of the loans? (Assume payments are made once per month.)

Ultimately, I want to know how should I distribute M over the 4 loans each month. Does anyone have a formula that can be used to approach this problem?
Click to expand...

Do you want to keep the same distribution of "M" each month, or do you want to vary that distribution over time?
 
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