## Additional Detail on Present and Future Values

This section gives more detail on computing present and future values. It shows you how to compute more complex problems involving future and present values when there are multiple compounding periods and when the time duration of those problems are longer or are less than one year.

### Loans and Loan Amortization

When paying off a debt, a portion of each payment is for interest while the remaining amount is applied towards the principal balance and amortized.

#### LEARNING OBJECTIVE

• Discuss the process of amortizing a loan

#### KEY TAKEAWAYS

##### Key Points
• Each amortization payment should be equal in size and pays off a portion of the principal as well as a portion of the interest.
• The percentage of interest versus principal in each payment is determined in an amortization schedule.
• If the repayment model for a loan is "fully amortized," then the very last payment pays off all remaining principal and interest on the loan.

##### Key Terms
• amortized loan: a form of debt where the principal is paid down over the life of the debt according to some amortization schedule, typically through equal payments
• amortization: the distribution of the cost of an intangible asset, such as an intellectual property right, over the projected useful life of the asset.
• amortization schedule: a table detailing each periodic payment over the life of the loan

In order to pay off a loan, the debtor must pay off not only the principal but also the interest. Since interest accrues on both the principal and previously accrued interest, paying off a loan can seem like a dance between paying off the principal fast enough to reduce the amount of interest without having huge payments. There is an incentive to paying off the loan ahead of schedule (lower total cost due to less accrued interest), but there is also a disincentive (less use of the principal). After all, if the debtor had enough money and liquidity to pay off the loan instantly, s/he wouldn't have needed the loan.

The process of figuring out how much to pay each month is called "amortization". Amortization refers to the process of paying off a debt (often from a loan or mortgage) over time through regular payments. A portion of each payment is for interest while the remaining amount is applied towards the principal balance.

In order to figure out how much to pay off to amortize each month, many lenders offer their debtors an amortization schedule. An amortization schedule is a table detailing each periodic payment on an amortizing loan, as generated by an amortization calculator. The typical loan amortization schedule offers a summary of the number of moths left for loan, interest paid, etc. The percentage of interest versus principal in each payment is determined in an amortization schedule .These schedules makes it easier for the person who has to repay the loan, s/he can calculate and work accordingly.

Period Interest Principal Balance
1 $583.33$191.97 $99,808.03 2$582.21 $193.09$99,614.95
3 $581.09$194.21 $99,420.74 4$579.95 $195.34$99,225.39
5 $578.81$196.48 $99,028.91 6$577.67 $197.63$98,831.28
7 $576.52$198.78 $98,632.50 8$575.36 $199.94$98,432.55
9 $574.19$20.11 $98,231.44 10$573.02 $202.28$98,029.16
11 $571.84$203.46 $97,825.70 12$570.65 $204.65$97,621.05
13 $569.46$205.84 $97,415.21 14$568.26 $207.04$97,208.16
15 $567.05$208.25 $97,999.91 16$565.83
$209.47$96,790.45
17 $564.61$210.69 $96,579.76 18$563.38 $211.92$96,367.84
19 $562.15$213.15 $96,154.69 20$560.90 $214.40$95,940.29
21 $559.65$215.65 $95,724.64 22$558.39 $216.91$95,507.74
23 $557.13$218.17 $95,289.57 24$555.86 $219.44$95,070.13

Amortization Schedule: An example of an amortization schedule of a \$100,000 loan over the first two years.

If the repayment model for a loan is "fully amortized," then the very last payment (which, if the schedule was calculated correctly, should be equal to all others) pays off all remaining principal and interest on the loan.