INTEREST (Simple Interest)
Interest is the sum paid for the use of borrowed money.
Interest is computed having the formula shown below.
Formula: I = PRT
Where:
I = Interest
P = Principal (face value)
R = Rate
T = Time (usually in years)
There are two types of Interest:
1. Ordinary - this is the interest computed for a given number of days divided by 360 as assumption.
Formula:
2. Exact - this is the interest computed for a given number of days divided by 365 as actual days in a year.
Final amount - is the sum of Interest and the principal.
Formula:
F = P + I
Where:
F = Final amount
P = Principal
I= Interest
Illustrative Examples:
1. Find the Interest and the Final amount on $3000 for 2 years at 5%.
Given:
P = $3000
R = 5% = 0.05
T = 3 years
Required:
I = (to be solved)
F= (to be solved)
Solution:
= $3000 * 0.05 * 3
= $450 (this is for interest only,not final answer)
Now, computing for Final amount:
F = P + I
= $3000 + $450
= $3450 (Final Answer)
So the interest for $3000 @ 5% for 3 years is $450 and the final amount is $3450.
2. How much interest is due on $2500 at 4.5% for 2 years and 6 months?
Given:
P = $2500
R = 4.5% = 0.045
T = 2.5
Required:
I = (to be solved)
F= (to be solved)
Solution:
Formula:
Now, computing for Final amount:
F = P + I
F = $2500 + $281.25
F = $2781.25 (Final Answer)
So the interest for $2500 @ 4.5% for 2.5 years is $281.25 and the final amount is $2781.25.
3. Find the interest for $5000 at 3.6% for 20 months.
In this example notice that the time (t) is not in years as SOP. In this case we need to change the "months" to years or simply y conversion.
Conversion:
1 year = 12 months
So,
20 months * 1 year / 12 months = 1.67 years.
Applying the given for the formula I = Prt:
Given:
I =
P= $5000
r= 3.6% = 0.036
t = 1.67
Required: Interest (I)
Solution:
I = Prt
I = $5000 * 0.036 * 1.67
I = $300.6 (Final answer)
4. What the exact interest on a loan of $7000 at 8.5% annual simple interest for 210 days?
Here, the problem stated the "exact" interest. Based on above condition, given days should be
divided to 365.
Hence,
210 / 365 = 0.575 as your time (t)
Solving the problem:
Given:
I = ?
P = $7000
r = 8.5% = 0.085
t = 0.575
Required: Exact Interest (Ie)
Solution:
By applying the formula:
Ie = Prt
Ie = $7000*0.085*0.575
Ie = $342.125 (Final Answer)
5. Peter loaned an amount of $10,000 from his friend John, with 2.5% ordinary interest for 2 years. Find the total amount should Peter paid to John 250 days.
In this example, the problem was in "ordinary" interest. Based on the condition, "days" should be converted to years by dividing it to 360.
So,
250 / 360 = 0.69 as your time (t)
Now, solving the problem.
Given:
I = ?
P = $10,000
r = 2.5% = 0.025
t = 0.69
Required: Ordinary Interest (Io)
Solution:
Formula: Io = Prt
Io = $10,000*0.025*0.69
Io = $172.5 (This is just an interest, not a final answer)
Final Amount Formula:
F = P + I
F = $10,000 + $172.5
F = $ 10, 172.50 (Final Answer)
Exercises:
1. What is the interest of money amounted to 7500 @ 3.46% for 2 years and 3 months?
2. Find the Interest and the Final amount on $6700 for 3 years at 6.5%.
3, How much interest will be charged on a loan of $12,640 for 60 days at an interest rate of
9.5%?
4. How much interest it will cost John to borrow %11,000 for 3 months at interest rate of
12%?
5. If $ 7,000 is invested at 11% simple interest for 6 years, what is the final amount?
6. Follow the instruction to supply the missing in the table below.
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