Question

QUESTION: For a given positive interest rate, the future value of $100 increases with the passage of time. Thus, the longer the period of time, the greater the future value.

ANSWER OPTIONS: True False

You need to specifically state IN THE SUBJECT LINE if the answer is TRUE or FALSE.  

EXAMPLES OF INADEQUATE RESPONSES: “I think the answer is False.” OR “The correct answer is “C.”

Postings must be no less than 200 words in length to be considered. Any posting less than 200 words in length will not be reviewed.

Answer 1

True

Given, Present value = $100; interest rate = positive (say 'r') ; period of compounding = t (assume)

Therefore, Future value = 100(1+r)^t . As we can see the future value will go on increasing if both the rate of interest 'r' and the period 't' are positive. Therefore, the longer the period of time, the greater will be the future value.

Future value is the value of an asset at a specific date. It measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain interest rate, or more generally, rate of return; it is the present value multiplied by the accumulation function.The value does not include corrections for inflation or other factors that affect the true value of money in the future. This is used in time value of money calculations.

Money value fluctuates over time: $100 today has a different value than $100 in five years. This is because one can invest $100 today in an interest-bearing bank account or any other investment, and that money will grow/shrink due to the rate of return. Also, if $100 today allows the purchase of an item, it is possible that $100 will not be enough to purchase the same item in five years, because of inflation (increase in purchase price).

An investor who has some money has two options: to spend it right now or to invest it. The financial compensation for saving it (and not spending it) is that the money value will accrue through the interests that he will receive from a borrower (the bank account on which he has the money deposited).

Therefore, to evaluate the real worthiness of an amount of money today after a given period of time, economic agents compound the amount of money at a given interest rate. Most actuarial calculations use the risk-free interest rate which corresponds the minimum guaranteed rate provided the bank's saving account, for example. If one wants to compare their change in purchasing power, then they should use the real interest rate (nominal interest rate minus inflation rate).

The operation of evaluating a present value into the future value is called capitalization (how much will $100 today be worth in 5 years?). The reverse operation which consists in evaluating the present value of a future amount of money is called a discounting (how much $100 that will be received in 5 years- at a lottery, for example -are worth today?).

It follows that if one has to choose between receiving $100 today and $100 in one year, the rational decision is to cash the $100 today. If the money is to be received in one year and assuming the savings account interest rate is 5%, the person has to be offered at least $105 in one year so that two options are equivalent (either receiving $100 today or receiving $105 in one year). This is because if you have cash of $100 today and deposit in your savings account, you will have $105 in one year