Estimating Repayment Time for Changing Borrowing and Repayments

Summary

The document asks how to calculate repayment rate and time to repay when a borrower takes out and repays multiple amounts at different dates. In particular, it asks how repayment timing might be weighted by the amounts borrowed and repaid. The response frames the issue using credit-card billing practices, where a minimum payment can include current interest plus a portion of the outstanding balance, subject to a floor.

It describes an amortization test as a way to estimate how long a representative balance would take to pay down if the borrower made minimum payments and took no further advances. Such a test can help assess the effective amortization period and detect negative amortization, where the balance grows. However, the response does not give a weighted payback-rate formula, calculate a weighted repayment period for staggered cash flows, or address how additional borrowing changes the estimate. Its guidance is a broad analogy rather than a complete calculation method.

Key ideas

• Credit-card minimum payments may combine interest with a portion of the outstanding balance, subject to a floor.
• An amortization test can estimate payoff time under an assumed repayment rule and no further borrowing.
• The test can help identify negative amortization, when the balance grows instead of shrinking.
• The response does not provide a formula for weighting repayment time across multiple borrowing and repayment events.

Tags

# How to calculate a weighted payback rate and period?


# How to calculate a weighted payback rate and period?












I have a client who borrows and repays money at different times. Assume the following example

What is the correct way to calculate the repayment rate and more importantly, the time until repayment (i.e. how long does it take to pay back a the borrowed amount) when there are multiple borrowing and repayment activities? How can I weight the time until repayment by the amount that is being borrowed and repaid?

## Answer by Magic is in the chain (score 2)

https://quant.stackexchange.com/a/46817

This is a typical situation the credit card providers face so I will answer with their approach. Their billing cycle is usually monthly, so at the point of billing they would calculate the minimum repayment amount, which would be the monthly interest times the current balance plus a proportion of the current outstanding balance with some floor.

In the background they would run Amortization tests on typical balances- essentially checking how long will it take for a typical balance to amortise if the cardholders repay minimum repayment amount as above, assuming no further withdrawals. The aim is to avoid negative Amortization, balance growing, but you can use concept of average life to check the effective Amortization period.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.