Loans

Study guide: Exam FM-2

A loan is a financial arrangement in which a lender provides Principal to a borrower, who repays the amount with Interest over time according to agreed terms. Key loan concepts include:

• Principal: the initial amount borrowed
• Interest Rate: the cost of borrowing per period
• Term of Loan: the number of periods over which the loan is repaid
• Outstanding Balance: the remaining principal at any point in time
• Amortization: the process of repaying a loan through a series of payments
• Final Payment: the last payment, which may differ from the regular payment — a smaller Drop Payment or a larger Balloon Payment

The Outstanding Balance at any time is computed by either of two equivalent methods: the prospective method (present value of the remaining payments) or the retrospective method (the loan accumulated to that date, less the accumulated value of the payments already made).

Monthly Mortgage Payment A 200{,}000 mortgage is repaid with level monthly payments over 30 years at a nominal rate of 6% convertible monthly. Find the monthly payment.

Answer Monthly rate: i^{(12)}/12 = 0.06/12 = 0.5\%. Number of payments: n=360. P = \frac{200{,}000}{a_{\overline{360}|0.5\%}} = \frac{200{,}000}{166.792} = 1199.10 \text{ per month}