hard · Principles of Finance time-value-of-money
A 30-year level-payment fully-amortizing loan and a 30-year interest-only-then-balloon loan are written on the same principal at the same fixed periodic rate i>0, with monthly payments. An analyst claims: 'Discounted at the contract rate i, the present value of all scheduled payments is identical for the two loans, because both repay the same principal.'
Is the claim correct, and why?
- Correct — both payment streams discount at i to exactly the original principal, since by no-arbitrage any schedule that repays the loan at its contract rate has present value equal to the amount borrowed.
- Incorrect — the interest-only loan has a higher present value at rate i, because its large terminal balloon payment is discounted less heavily than the amortizing loan's earlier, front-loaded principal.
- Incorrect — the amortizing loan has a higher present value at rate i, because returning principal sooner is worth more in present-value terms than waiting for the deferred balloon payment.
- Correct in present-value terms, but only because the interest-only loan pays strictly more total nominal interest, which exactly offsets the payment deferral once discounted at rate i.
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