IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Practical applications of the equation of value (loans and APR)
A lender charges the same flat rate of 10% per annum on a 3-year loan, and the total interest is therefore fixed. Which statement about the effective rate (APR) is correct?
The APR is higher with monthly repayments than with annual ones. Flat interest is charged on the original loan, so the total interest is the same, but monthly instalments repay the principal sooner and lower the average balance outstanding. The same interest on a smaller balance means a higher effective rate.
- AThe APR is always lower than the flat rate, however the loan is repaid
- BThe APR is the same whether repayments are annual or monthly, since the total interest is fixed
- CThe flat rate is calculated on the outstanding balance after each instalment
- DThe APR is higher when repayments are monthly than when they are annual, because the balance is repaid soonerCorrect
- The APR equals the flat rate whenever the loan is repaid in instalments
Explanation
With a fixed total of flat interest, more frequent instalments reduce the average outstanding balance, so the same interest cost is spread over a smaller balance and the effective rate is higher. The APR exceeds the flat rate for instalment loans, so the first option is wrong. Flat interest is charged on the original principal, not the reducing balance.
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