How does a loan reduce to zero when interest is charged and regular repayments are made?
Model a reducing-balance loan with a recurrence relation, build an amortisation table, and find balances, repayments and total interest.
How to model a reducing-balance loan with a recurrence relation, read and build an amortisation table, and find the balance, repayment and total interest paid.
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What this dot point is asking
You must set up the loan recurrence, build or read an amortisation table, and find balances, repayment size and total interest.
The loan recurrence
A reducing-balance loan combines compound interest with a regular repayment.
Each period the balance first grows by interest, then the repayment is taken off. If the repayment exceeds the interest, the balance falls; this is what eventually clears the loan.
The amortisation table
An amortisation table records each period's interest, principal reduction and new balance.
Total interest paid
Over the life of the loan, the total interest is the sum of all repayments minus the amount borrowed. This is usually far more than first-time borrowers expect, which is the point such questions make.
Choosing the repayment
If the repayment only just covers the interest, the balance barely moves and the loan never clears; if it is below the interest, the balance grows. A repayment must exceed the first period's interest for the loan to reduce at all, a useful sanity check.