If the interest rate is positive, then the future value of an annuity due will be greater than the future value of an ordinary annuity.

Question

BlackTom AI · Accepted Answer

Question restatement: If the interest rate is positive, then the future value of an annuity due will be greater than the future value of an ordinary annuity. Answer options: True, False.
Option 1 (True): With a positive interest rate, each payment in an annuity due earns interest for one more period than the corresponding payment in an ordinary annuity, because payments are made at the beginning of the period. Consequently, the future value formula for an annuity due is the future value of an ordinary annuity multiplied by (1 + i). Since i > 0, multiplying by (1 + i) increases the value, making the annuity due’s FV larger than the ordinary annuity’s FV.
Option 2 (False): This statement would be correct only if the interest rate were zero or negative. When i > 0, the extra period of interest on every payment in the annuity due accumulates, so this option misstates the relationship between the two FVs.
Additional nuance: If the interest rate were zero, both future values would be equal regardless of payment timing, but the given condition specifies a positive rate, which drives the FV of the annuity due above the ordinary annuity. In general terms, the gap between the two FVs widens as i increases above zero.
In summary, under a positive interest rate, the annuity due accumulates a larger future value than the ordinary annuity because each payment sits one more period in the interest-earning timeline.

If the interest rate is positive, then the future value of an annuity due will be greater than the future value of an ordinary annuity.判断题

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