Essay on Time Value of Money and Payment

Fundamentals of Financial Management

This table and its concept should be understood, or learned by most, as Brigham and Houston (2007) explain amortized loans are common and widely used for auto, mortgage, student and a lot of business loans. Amortization is the repayment of a loan in equal amounts in either “monthly, quarterly, or annual basis” according to Brigham and Houston (2007). For this scenario we will go with an automobile loan.

This table provides us with the total amount borrowed, how many years the loan will be in repayment, the interest rate applied, and the payment (in this case is given on a yearly basis). Beginning in year one the loan is granted for a total of $100,000. Annual payments totally $23,739.64, from this amount $17,739.64 is directed towards the principal amount, and $6,000 goes towards interest. Within this table we can see that each year, the beginning amount, interest portion and ending balance all decrease and the only number that increases is the amount of the payment that is paid towards the principal.

Comparing this table to the TVM (time value of money) shown in the other tables, we can see the application here is that $100,000 today (with the given loan parameters) is equal to $118,698.2 in five years. In table 2.1 the future value of a $100 payment is used to understand the value of that payment within three years; where table 2.2 does the opposite looking at the payment starting in year three, and breaking it down to see its present value. Table 2.3 depicts the future value of a typical annuity, which includes looking at an account in which equal deposits are made for three years, and the interest applied to each is 5%.

To solve this problem on the calculator complete the steps as follows (this will give the first year information)

Make sure your work is cleared

Hit 2nd, P/Y, #1 enter -------this gives us one payment per year

2nd, quit

#5, 2nd, xP/Y, N ----- this gives us five years of payments

#100,000 PV, 6.00 I/Y---- this sets the loan amount, and interest rate

CPT, PMT -- this displays the amortized payment amount

To get the amortization schedule hit 2nd, AMORT

The P will stay at one, press the down arrow key, and 1 again then down arrow again

This gives the ending balance for year one, principle amount paid and interest paid. Continue with the down arrow for subsequent year schedules.

Microsoft Excel—

Fill in the required information in the cells on the top right (column A & B)

In my example I chose to lower the schedule so that the formula would pull from the top and include the rest of the information that brings the principal, interest and balance.

In Column B, cell 7, I have used the PMT function to compute the annual payment. PPMT function to calculate the principal amount, the IPMT function will calculate in the interest cells, and in the balance section type in =Amount+C7

Below is the result

Annual Interest Rate 6.00% Years 5 Payments Per Year 1 Amount $100,000

Payment Number Payment Principal Interest Balance 1 ($23,739.64) ($17,739.64) ($6,000.00) $82,260.36 2 ($23,739.64) ($18,804.02) ($4,935.62) $63,456.34 3 ($23,739.64) ($19,932.26) ($3,807.38) $43,524.08

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