User:Brett epic/sandbox

Formula for calculating compound interest:

$$A = P\left(1 + \frac{r}{n}\right)^{nt}$$

Where,
 * P = principal amount (initial investment)
 * r = annual nominal interest rate (as a decimal)
 * n = number of times the interest is compounded per year
 * t = number of years
 * A = amount after time t

Example usage: An amount of $1,500.00 is deposited in a bank paying an annual interest rate of 4.3%, compounded quarterly. Find the balance after 6 years.

A. Using the formula above, with P = 1500, r = 4.3/100 = 0.043, n = 4, and t = 6:

$$A=1500\left(1 + \frac{0.043}{4}\right)^{4 \cdot 6} =1938.84$$

So, the balance after 6 years is approximately $1,938.84.

$$ p = \frac{P_0*r^{(n+1)}}{\sum_{l=1}^n r^l} $$
 * where:
 * $$ P_0 $$ is the initial principal
 * $$ r $$ is the percentage rate used each payment
 * $$ n $$ is the number of payments

Flat interest rate loans are often used by traditional moneylenders in the informal economy of developing countries. They are also used by many microfinance institutions. One reason for their popularity is their ease of use. For example, a loan of $1,200 can be structured with 12 monthly repayments of $100, plus interest, due on the same dates, of 1% ($12) a month, resulting in a total monthly payment of $112. In the example to the right, the loan contract is for 400,000 Cambodian riels over 4 months. Interest is set at 16,000 riels (4%) a month while principal is due in a single payment at the end.

Flat rate calculations, which are based on the amount of money the borrower receives at the beginning of the loan rather the average amount the borrow has access to during the loan, have been outlawed in developed countries (see for example the Truth in Lending Act). However, they persist in many developing countries, and have frequently been adopted by microcredit institutions.

They are also sometimes used by on-line microlending operators. For example, kiva.org quotes interest rates as the "self reported average, annualized, flat interest rate in real terms charged by the Field Partner to the enterpreneur." For a variety of reasons (see below), flat rates can be useful in lending to poor people, and often disappear very slowly as financial systems develop.

Flat rate calculations
To use the example above, the borrower only has access to $1,200 at the very beginning of the loan. Since $100 in principal is being paid each month, the average amount the borrower has access to during the loan term is actually slightly more than half of $1,200. This means that the effective interest on such a loan, if recalculated using the declining balance method, is nearly double the flat rate.

In the first 3 examples on the right the borrower will be quoted 1% a month. These are loans of $1,200 each, amortized with level payments over 4, 12 and 24 months. In the 4-month example, the borrower will make 4 equal payments of $300 in principal and 4 equal payments of $12 (1% of $1,200) in interest. This yields an annualized flat rate of 12%, and an annualized effective APR of 19.05%.

To keep the quoted interest rate as low as possible, microcredit institutions often recover some of their lending costs by charging one-time origination or administration fees before disbursing loans. Because these fees are deemed an inherent cost of borrowing, developed countries generally require lenders to include them in APR calculations. Even an origination fee as low as 4% of the total loan can have a large impact on the borrower's total costs. This is especially true for short-term loans, as the last 3 examples in the table show. Microcredit loans are usually for 12 months or less.

In order to recalculate a flat rate as an effective APR, it is necessary to model a comparable loan using a declining balance amortization schedule, resulting in the same total cost to the borrower (see table on the left). The loan is for $1,200 repayable in level monthly payments over 4 months. The total cost of this loan includes the principal plus $48.00 in interest. The effective APR is calculated by iteration from the amortization schedule, using the compound interest formula.

Benefits of flat rate lending
Flat interest rates persist in emerging and informal financial systems due to the following advantages:


 * They are easy to calculate and track: Flat interest rates require no calculations to blend principal and interest into a level payment, and require no compounding calculations (see the example to the right).  Traditional moneylenders often do not have either computers or calculators, and neither do their borrowers, who are often illiterate and/or innumerate.  Flat rates keep loan commitments clear, transparent and easily tracked by both parties.  Many microfinance institutions do not have computers either, and the complexity of declining balance calculations may confuse their borrowers and even their staff.  Semi-formal institutions like self-help groups, village banks and ASCAs also usually prefer this calculation method.


 * They meet vital cash flow needs of farmers: Many borrowers in developing countries are farmers who demand loans with balloon payments, repayable after they harvest their crops.  Because the borrower is using the entire amount of principal borrowed throughout the entire loan term, flat rate calculations are accurate when applied to balloon loans.


 * They support 'in-kind' loan transactions: Flat rate loans originated before currency was invented, and are commonly used to repay loans in regular instalments of chickens, eggs, kilos of rice, and so on.  For farmers accustomed to these types of transactions, flat rate cash loans are familiar and easy to understand.

Problems with flat rate lending
Flat interest rates represent a significant problem for financial sector development for the following reasons:


 * They deter pre-payments by borrowers: Borrowers have an incentive to avoid pre-paying flat-rate loans, as they will lose the use of the borrowed money with no compensating discount in interest payments.  Lenders are therefore ensured maximum interest income, which encourages them to continue the practice.  Writing of the practices of microfinance institutions in Bangladesh, S.M. Rahman points out that "[i]f one client takes a loan today and offers to repay the entire loan the next day, the client has to repay the total loan along with the whole year's interest, reckoned on a flat rate system."


 * They offer convenient level of disclosure for the lender (but not for the borrower): Flat interest rates generally prevail only where declining balance calculations are not familiar to most borrowers, or are not required by law.  In such places loans quoted using declining balance rates may be rejected by borrowers, who mistakenly believe that flat rates are cheaper.  "Not only the clients but even educated people sometimes have trouble understanding this system.  The problem is that the flat rate gives an impression of a lower rate than it actually is."

In addition, MFIs that use flat rates calculations are slightly understating the size of their outstanding loan portfolios, which results in the appearance of a higher portfolio yield and lower average loan sizes. Both of these characteristics appeal to donors and external financiers.

Towards consumer protection in borrowing
The less developed an economy, the more active informal moneylenders usually are, and the less capacity the government may have to regulate them effectively. As a result, Brigit Helms argues for an evolutionary approach to interest rates, in which they can be expected to gradually drop as competition increases and the government gains greater capacity to effectively enforce comparable interest rate disclosures on financial sector actors. At the same time, interest rate ceilings, and popular conflation of flat rates with declining balance ones, has led many microfinance institutions to replace interest rate points with transaction fees and other charges.