Question:
Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
Correct Answer
$10070
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5300 × 9% × 10
= $5300 ×9/100 × 10
= 5300 × 9 × 10/100
= 47700 × 10/100
= 477000/100
= $4770
Thus, Simple Interest = $4770
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $4770
= $10070
Thus, Amount to be paid = $10070 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5300
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5300 + ($5300 × 9% × 10)
= $5300 + ($5300 ×9/100 × 10)
= $5300 + (5300 × 9 × 10/100)
= $5300 + (47700 × 10/100)
= $5300 + (477000/100)
= $5300 + $4770 = $10070
Thus, Amount (A) to be paid = $10070 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5300, the simple interest in 1 year
= 9/100 × 5300
= 9 × 5300/100
= 47700/100 = $477
Thus, simple interest for 1 year = $477
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $477 × 10 = $4770
Thus, Simple Interest (SI) = $4770
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $4770
= $10070
Thus, Amount to be paid = $10070 Answer
Similar Questions
(1) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 4 years.
(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.
(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 7 years.
(5) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 4 years.
(6) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.
(7) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(9) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(10) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.