in how much time will the simple interest on $16000 at rate of 5% per annum be the same as the simple interest on $20000 at rate of 10%per annum for 8 years
Answers
Answer:
Do you know that banks pay you to let them keep your money? The money you put in the bank is called the principal, P , and the bank pays you interest, I . The interest is computed as a certain percent of the principal; called the rate of interest, r . The rate of interest is usually expressed as a percent per year, and is calculated by using the decimal equivalent of the percent. The variable for time, t, represents the number of years the money is left in the account.
Definition: simple interest
If an amount of money, P , the principal, is invested for a period of t years at an annual interest rate r, the amount of interest, I , earned is
I=Prt
where
I = interest
P = principal
r = rate
t = time
Interest earned according to this formula is called simple interest.
The formula we use to calculate simple interest is I = Prt. To use the simple interest formula we substitute in the values for variables that are given, and then solve for the unknown variable. It may be helpful to organize the information by listing all four variables and filling in the given information.
Example 6.4.1
Find the simple interest earned after 3 years on $500 at an interest rate of 6%.
Solution
Organize the given information in a list.
I = ?, P = $500, r = 6%, t = 3 years
We will use the simple interest formula to find the interest.
Write the formula.
I = Prt
Substitute the given information. Remember to write the percent in decimal form.
I = (500)(0.06)(3)
Simplify.
I = 90
Check your answer. Is $90 a reasonable interest earned on $500 in 3 years?
In 3 years the money earned 18%. If we rounded to 20%, the interest would have been 500(0.20) or $100. Yes, $90 is reasonable.
Write a complete sentence that answers the question.
The simple interest is $90.
Exercise 6.4.1 :
Find the simple interest earned after 4 years on $800 at an interest rate of 5%.
Answer
Exercise 6.4.2 :
Find the simple interest earned after 2 years on $700 at an interest rate of 4%.
Answer
In the next example, we will use the simple interest formula to find the principal.
Example 6.4.2 :
Find the principal invested if $178 interest was earned in 2 years at an interest rate of 4%.
Solution
Organize the given information in a list.
I = $178, P = ?, r = 4%, t = 2 years
We will use the simple interest formula to find the principal.
Write the formula.
I = Prt
Substitute the given information.
178 = P(0.04)(2)
Divide.
1780.08=0.08P0.08(6.4.1)
Simplify.
2,225 = P
Check your answer. Is it reasonable that $2,225 would earn $178 in 2 years?
178=?2,225(0.04)(2)(6.4.2)
178=178✓(6.4.3)
Write a complete sentence that answers the question.
The principal is $2,225.
Exercise 6.4.3 :
Find the principal invested if $495 interest was earned in 3 years at an interest rate of 6%.
Answer
Exercise 6.4.4
Find the principal invested if $1,246 interest was earned in 5 years at an interest rate of 7%.
Answer
Now we will solve for the rate of interest.
Example 6.4.3
Find the rate if a principal of $8,200 earned $3,772 interest in 4 years.
Solution
Organize the given information.
I = $3,772, P = $8,200, r = ?, t = 4 years
We will use the simple interest formula to find the rate.
Write the formula.
I = Prt
Substitute the given information.
3,772 = 8,200r(4)
Multiply.
3,772 = 32,800r
Divide.
3,77232,800=32,800r32,800(6.4.4)
Simplify.
0.115 = r
Write as a percent.
11.5% = r
Check your answer. Is 11.5% a reasonable rate if $3,772 was earned in 4 years?
3,772=?8,200(0.115)(4)(6.4.5)
3,772=3,772✓(6.4.6)
Write a complete sentence that answers the question.
The rate was 11.5%.
Exercise 6.4.5 :
Find the rate if a principal of $5,000 earned $1,350 interest in 6 years.
Answer
Exercise 6.4.6 :
Find the rate if a principal of $9,000 earned $1,755 interest in 3 years.
Answer
Solve Simple Interest Applications
Applications with simple interest usually involve either investing money or borrowing money. To solve these applications, we continue to use the same strategy for applications that we have used earlier in this chapter. The only difference is that in place of translating to get an equation, we can use the simple interest formula.
We will start by solving a simple interest application to find the interest.
Example 6.4.4 :
Nathaly deposited $12,500 in her bank account where it will earn 4% interest. How much interest will Nathaly earn in 5 years?
Solution
We are asked to find the Interest, I. Organize the given information in a list.
I = ?, P = $12,500, r = 4%, t = 5 years
Write the formula.
I = Prt
Substitute the given information.
I = (12,500)(0.04)(5)
Simplify.