Time Value of Money

Time Value of Money
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Pearland Medical Center has just borrowed $1,000,000 on a five-year loan with annual payment term at a 12 percent rate. The first payment will be due one year from now.
Amortization schedule for this loan
The loan payment formula is based on the ordinary annuity formula, given that there are future periodic payments to be made annually. The monthly payments is calculated A=i*P (1+i) n/ (1+i) n-1 which is $ 22,244.45. However, this is an annual payment and the amount payable is P= PV/ PVIFA.
PV=$1,000, 000 and hence P= 1,000,000/ 3.6048= 277,407.73
The staring interest rate is 12% of 1,000,000 being 120,000
The subsequent interest rates for year 2 to 5 are 12% of the ending balance form the previous year (beginning balance of that year)
DatePmt #PaymentPrincipalInterestBalanceStarting Balance$1,000,000.00 Year 11$277,409.73 $157,409.73 $120,000.00 $842,590.27 Year 22$277,409.73 $176,298.90 $101,110.83 $666,291.37 Year 33$277,409.73 $197,454.77 $79,954.96 $468,836.60 Year 44$277,409.73 $221,149.34 $56,260.39 $247,687.26 Year 5 5$277,409.73 $247,687.26 $29,722.47 $0.00 Total5 Pmts$1,387,048.66 $1,000,000.00 $387,048.66  
The calculation takes into account the periodic payments of the principal amount over the life of the loan in equal periods of five years. However it was necessary to first calculate the monthly interest payment. In any case, since, the principal amount is paid first and then he periodic payments paid over the life of the loan, the amortization is merely the calculation of these periodic payments. Hence the frequency of the payment yearly, amount borrowed, terms of the loan and the interest rates are necessary to carry out the calculation.
Changes after amortization
In the loan amortization each loan payment is made up of interest payments and the loan principal. As such, the allocation of the loan payment allocation for interest and the principal differs for the different payment periods, but the loan payment stays constant. The portion representing interest declines over time while the portion going to the principal amount increases. Since the interest payment is based on the beginning balance which is lower than the previous year after payments, then it follow that the interest will also be lower. On the other hand, since the principal is the difference between the loan payment and interest payment, it follows that the amount will increase.
In the time value of money then the process of loan amortization focuses on finding the streams of payments over the term of the loan with a present value that is represented by the inters rate (Graham, Smart, & Megginson, 2010). As such, the amortization schedule captures the information on t...