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Which of the following statements is true?

a. The process of discounting is the inverse of the process of compounding.
b. Ending balances using simple interest are always greater than ending balances using compound interest at positive interest rates.
c. The present value of an annuity due is always less than the present value of an equivalent ordinary annuity at positive interest rates.
d. The future value of an annuity due is always less than the present value of an equivalent ordinary annuity at positive interest rates.

User Lashonne
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1 Answer

7 votes

Final answer:

The correct response is that the process of discounting is the inverse of the process of compounding. The other statements provided are incorrect as they misunderstand the comparative values of interest calculations for simple and compound interest, and for present and future values of annuities due and ordinary annuities.

Step-by-step explanation:

The correct statement is: a. The process of discounting is the inverse of the process of compounding.

Discounting is a financial concept that involves determining the present value of a future amount by applying a discount rate. It is used to compare the value of future cash flows to today's dollars. When discounting, you essentially reverse the compounding process, which is the calculation of the future value of an amount of money or a stream of cash flows given a specific rate of return. In compounding, the interest earned is reinvested to earn additional interest, and this effect accumulates over time.

Statement b is incorrect because, at positive interest rates, compound interest, which takes into account the interest on interest, generally leads to a higher ending balance compared to simple interest, which only applies to the principal.

Statement c is also incorrect as the present value of an annuity due, which begins immediately, is higher than the present value of an equivalent ordinary annuity, which begins at the end of the first period.

Statement d is incorrect because the future value of an annuity due is greater than that of an ordinary annuity since payments for an annuity due are made at the beginning of each period, which allows more time for the money to grow through compounding.

User Bachonk
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