pv of annuity table
Amortized loans are the loans that are to be repaid in equal periodic amounts (monthly, quarterly or annually). Amortization tables reflect the relationships between, principal, interest, number of periods and payment. Principal is the amount due, which satisfies the payoff of the underlying obligation, interest is the percentage paid for the use of money and number of periods is the maturity of the loan.
Example
Suppose a firm borrows $1,000 and the firm must amortize the loan over 3 years with equal end-of-year payments. The lender charges a 6% interest rate on the loan balance that is outstanding at the beginning of each year. In order to determine the amount the firm must repay each year, an amortization schedule is setup that shows the annual payments and the amount of each payment to pays off the principal and the amount that constitutes interest expense to the borrower and interest income to the lender. To determine the actual payments, the firm recognizes that the $1,000 represent the present value of an annuity of PMT dollars per year for three years, discounted at 6%.
There are three methods to calculate the payments for an amortization table.
1/ Numerical solution
Since we know the present value (PV = $1,000), the interest rate (r = 6%) and the number of periods (n = 3 years) we apply the following equation:
PV = PMT {1 – [1/ (1+r)^n]} / r => $1,000 = PMT {1 – [1/1+6%)^3 ]} / 6% => $1,000 = PMT (1 – 0.8396) / 6% => $1,000 = PMT (0.1604 / 6%) => $1,000 = PMT (2.6733) => PMT = $1,000 / 2.6733 => PMT = $374.07
2/ Financial calculator solution
In the financial calculator we enter the inputs N = 3, I = 6, PV = 1000 and FV = 0 and we press the PMT key which calculates the payment PMT = -374.07
3/ Spreadsheet solution
This is the ideal solution for developing an amortization table. To calculate the payments we use the function wizard. Assuming that I=6% is in cell B1, N=3 is in cell B2 and PV = 1000 is in cell B3, the function PMT (B1, B2, B3) would return a result of -374.07.
In amortization, initial payments always include more interest than principal. By and large, in an amortization schedule, the majority of payments apply to interest in the first years of the loan, with a small amount applied towards paying off the principal. As the loan reaches maturity and the principal decreases more payments apply to repaying the principal as the interest owed to the lender is decreased.
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