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Simple and Discount Interest

In financial transactions, interest is the amount paid by a borrower to a lender for the use of money over a period. Interestthat is paid as a percent of amount borrowed or invested is called simple interest. The formula for simple interest is given by the following:

Simple Interest

Where,

Example

1. Suppose an amount Php 500.00 is invested for 2 years at 6% per year. How much is the earning of the investment after two years?

Solution:
The following can be obtained from the problem:,,.
. From this we conclude that, the investment earned Php60.00.

2. If Php4, 000.00 is borrowed at an annual interest rate of 16% for 9 months. How much is the interest due in borrowing the amount of money?

Solution:
Given :
,,.

. From this we conclude that, the interest due is Php480.00.

Sometimes if we are the investor, we consider the value of our investment after a given period. In this case we introduce the concept of future values or accumulated values.

Future Value

Where,

Present Value
P = F(1+rt)-1 OR P = F ÷ (1+rt)

Example

1. If Php4, 000.00 is borrowed at an annual interest rate of 16% for 0.75 years, what is the value of the investment after 0.75 years?

Solution:
Since the interest earned by the amount invested for 0.75 years is Php480.00, the value of Php4,000.00 after 0.75 years is Php4,480.00.

2. What is the simple interest rate applied if an investment of Php37,500 accumulates to Php45,937.00 in the period of 1.5 years?

Solution:
We note that the interest earned by the investment is Php8, 437, that is,. From the formula, we have

3. The repayment on a loan was Php12,100. If the loan was for 15 months at 16.8% interest a year, how much was the principal?

Solution:
Based from the given we have the following: , , and
Since, we have.

Different ways of expressing time/term of a loan or investment.

Sometimes the term of investment is not given in years. The term or time frame given in certain problems maybe stated in days or months. In cases where the time is expressed in months it is easy to express it in years. But when the term/time is given in days we use a time factor such as the following: Ordinary Simple Interest or Bankers Rule

Exact Simple Interest

t =

t =

t =

t =

Examples:
1. Find the exact interest and the final amount due on P28,000 at 12% for 120 days. 2. Using ordinary interest, determine the final amount due on P10,800 at 15.5% for 100 days.

The Bankers Rule or Ordinary Simple Interest is applied whenever a given problem does not specify the time factor to be used.

Remark

Sometimes the term or time frame may be drawn from the specified origin and repayment dates. The following indicated how to compute for the actual time and approximate time.

Actual time – Number of days until the repayment date except the origin date. Approximate time – Assumes that every month contains 30 days.

Example
Find the actual and approximate time from May 1, 1983 to September 15, 1983. Actual Time
May30
June30
July31
Aug31
Sept15
137
Approximate Time
May29
June30
July30
Aug30
Sept15
134
31-1=30
30-1=29

Examples:
1. Find the approximate and actual number of days from March 15, 1993 to December 20 of the same year.
YearMonthDay
1993 12 20
Less:1993 3 15
0 9 5
Approximate No. of Days: (9 * 30) + 5 = 275 days

Simple Discount Interest.

Similar to simple interest, discount interest is an amount paid for borrowing money. Unlike simple interest, however, discount interest is charged at the time the loan...
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