Three questions and their implications

¶ … interest paid at the beginning of a loan period than at the end of the loan period?

Whether an equal total payment plan is adopted or an equal principle plan, in both cases the interest paid at the beginning of a loan repayment period is more than at the end. This is because the interest is calculated on the amount that is loaned. When the first payment is made then a specific principle amount that the borrower has paid for is deducted from the total loan given. Thus the total amount loaned reduces and hence the interest on the new amount is lesser for the second payment.

Using an example of an equal principle plan, if a borrower borrows $10,000 for a repayment plan of 10 years at the rate of 10% per annum, the premium will be divided equally in 10 parts. Which means that each year $1,000 will be deducted from the original loan. Hence interest for the first payment will be calculated as 10/100 x 10,000 = $1,000

Thus the total amount of the first payment will be $2,000. This includes $1,000 for the interest and another $1,000 which will be deducted from the original loan. This leaves the amount loaned to be $10,000 - $1,000 = $9,000.

For the second payment the interest would hence be calculated to be 10/100 x $9,000 = $900 and therefore the total amount to be paid at the second year would be $1,000 + $900 = $1,900. Similarly for the third year the total amount loaned will again be reduced to $9,000 - $1,000 = $8,000 and thus the interest paid will further reduce. This pattern will go on till the last year where the total amount loaned would be reduced to $1,000 with a more reduced interest paid.

As seen from the example given, the interest paid in the beginning of a loan period is high because the actual amount loaned is high. With time as the total amount loaned reduces, the interest paid reduces.

2) Is a dollar today worth more than a dollar tomorrow? Why or why not?

A dollar today is worth more than a dollar tomorrow. A simple fact is that any company would prefer to have a dollar today than tomorrow. This is because a dollar today can be invested and would earn a return thus increasing its value tomorrow. Another way to look at it is that a dollar can be kept in a bank and at the end of lets say 10 years, it would have increased thus increasing its value. This is simply referred to as the time value of money which can be expressed in other words that if today you lend someone a dollar today then tomorrow you will ask for its return with interest.

Further there is an important risk factor to consider - inflation. Inflation devours the buying power of money. You can buy more today than you would be able to tomorrow. Taking an example, if we are to take a dollar today and buy food, and compare it will a dollar, lets say 10 years from now and purchase food then, we will see that what can be bought today from that dollar would be much more than what can be bought from the same face value 10 years from now. This is the basic concept of what inflation is and how it reduces the value of money over a period of time. Thus a dollar in the present has a greater value than that of a dollar in the future.

3) What is the relationship between present and future value?

The time value of money tells us that a dollar today is worth more than a dollar tomorrow. Thus present value is an amount today which is equivalent to an amount paid in the future. In simpler words this means that the present value of a promised future amount keeps on decreasing with increasing time span. $10 promised to be paid after 5 years would have a greater present value than $10 to be paid after 10 years.

Therefore present value is simple where you determine the present value of $1,000 to be paid after 10 years or in other words it is the amount that you need to deposit in a bank such that after 5 years it accumulates to be $1,000.