IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Practical applications of the equation of value (loans and APR)
A finance company advertises a personal loan at a flat rate of 8% per annum, repaid in equal monthly instalments over 5 years. Which statement about the relationship between this flat rate and the annual percentage rate (APR) is correct?
The APR exceeds the flat rate. Flat interest is computed on the original principal for the whole term, while the amount actually owed falls with every instalment. The borrower thus pays interest on money already repaid, so the effective rate on the true balance is higher than the quoted flat rate.
- AThe APR exceeds the flat rate, because interest is charged on the original loan although the outstanding balance falls with each instalmentCorrect
- BThe APR equals the flat rate, because both are quoted per annum
- CThe APR is below the flat rate, because monthly repayments reduce the capital early
- DThe APR is independent of the repayment frequency but depends on the loan size
- The APR is below the flat rate only if the first instalment is paid in advance
Explanation
Under a flat rate, interest is calculated on the full original principal for the entire term. The borrower's actual outstanding balance reduces as instalments are paid, so the effective cost on the money actually still owed is higher. The APR therefore exceeds the flat rate, and the gap widens with more frequent repayments. Payment in advance would raise the APR even further.
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