Loan Balances and Refinancing

≈ 25 min

0/4 practice checks

Loan Balances and Refinancing

Immediately after a payment, the outstanding balance is the present value of remaining instalments. At a refinancing date, value the old debt and the new payment stream at that same focal date.

Worked reasoning

The balance values only the instalments still to come.
There are 24 such payments.
Therefore use $n=24$ .

Key idea

An outstanding balance is the present value of payments that have not yet been made.

A loan has 24 payments left. Immediately after a payment, which value of $n$ belongs in the present-value annuity formula for the balance?

Which statement best captures the central mathematical idea in Loan Balances and Refinancing?

An outstanding balance is the present value of payments that have not yet been made.

Outstanding balance equals the sum of payments already made.

A memorised formula is valid even when its conditions are not met.

The diagram or notation replaces the need to justify each mathematical step.

When starting a problem about Loan Balances and Refinancing, which move is most reliable?

Locate the balance date and count only the payments remaining after it.

Round every value before identifying the mathematical structure.

Choose the longest available formula and substitute immediately.

Assume the desired conclusion and work backwards without checking equivalence.

Which statement is a misconception that must be rejected when working with Loan Balances and Refinancing?

Outstanding balance equals the sum of payments already made.

An outstanding balance is the present value of payments that have not yet been made.

Locate the balance date and count only the payments remaining after it.

Rebuild the original loan as paid portion plus remaining present value at a common date.

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