Final answer:
The statement is false; the future value of an annuity due is typically higher than that of an ordinary annuity because payments are made at the beginning of each period, thus accruing more interest over time.
Step-by-step explanation:
The statement that the future value of an annuity due is equal to the future value of an ordinary annuity is false. An annuity due is a type of annuity payment where payments are made at the beginning of each period. Conversely, an ordinary annuity makes payments at the end of each period. These timing differences affect the future value calculation of each.
When calculating the future value, an annuity due will have one extra period of interest accruing because of the earlier payments, making its future value higher, assuming all else equal, compared to an ordinary annuity under the same interest rate and same term. These distinctions are critical in financial calculations, where the present and future values play a pivotal role in investment decisions and loan assessments.
Understanding this difference is important when considering the real-world calculations of financial products such as bonds, where the price a borrower can pay will reflect the present value of these future expected payments, accounting for factors like interest rates and default risk.