You are comparing two annuities that offer regular payments of $2,500 for five years and pay .75 percent interest per month. You will purchase one of these today with a single lump sum payment. Annuity A will pay you monthly, starting today, while Annuity B will pay monthly, starting one month from today. Which one of the following statements is correct concerning these two annuities?

Question

BlackTom AI · Accepted Answer

First, restate the setup: there are two 60-payment annuities of 2,500 each, with a monthly interest rate of 0.75% (i = 0.0075). Annuity A starts payments immediately (an annuity due), while Annuity B starts payments one month from today (an ordinary annuity). We will compare present values (PV) and future values (FV) to see how they differ between the two.

Option 1: Annuity B has a smaller present value than Annuity A. This aligns with the standard relationship PV_due = PV_ordinary × (1 + i). Since Annuity A is due, its present value is larger than Annuity B’s for the same payment amount, number of payments, and interest rate. The math is PV_due = 2,500 × [1 + i] × [1 − (1 + i)^−n]/i, while PV_ordinary = 2,500 × [1 − (1 + i)^−n]/i. Because (1 + i) > 1, PV_due > PV_ordinary, meaning Annuity B’s PV is indeed smaller.

Option 2: Annuity B is an annuity due. This is incorrect because Annuity B begins payments one month from today, which characterizes an ordinary annuity, not a due. Annuity due would have payments starting today.

Option 3: These two annuities have both equal present and equal future values. This is false given the timing difference. The initial payment timing creates a PV and FV advantage for the due version (Annuity A) over the ordinary version (Annuity B). Therefore neither PV nor FV are equal between the two.

Option 4: Annuity A has a smaller future value than Annuity B. This cannot be right because the future value of a due annuity is larger than that of an ordinary annuity when payments and terms are the same, since each payment is invested an extra period. Hence FV_A > FV_B, not smaller.

Option 5: These annuities have equal present values but unequal future values. This is contradicted by the standard relationship between PVs for due and ordinary annuities with identical terms and payments; the present values are not equal (PV_due > PV_ordinary), and the future values are also not equal (FV_due > FV_ordinary).

类似问题

Which type of annuity has payments that occur at the beginning of the period?

Which of the following best describes the difference between an annuity due and an ordinary annuity?

Which of the following statements is correct?

(4 marks, difficulty level: Easy) Suppose that you invest $28,000 in an account paying 8% interest. You plan to withdraw $2300 at the end of each year for 20 years. How much money will be left in the account after 20 years?

An annuity investment is formed when $500,000 is invested at a rate of interest of 3.1% per annum, compounded monthly.An additional payment of $1500 is made into the account each month. The value of the annuity after 5 years is closest to:

An ordinary annuity is best defined as:

An ordinary annuity is best defined as:

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