Question:
Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.
Correct Answer
$9780
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 9%
Time (t) = 7 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) = $6000 × 9% × 7
= $6000 ×9/100 × 7
= 6000 × 9 × 7/100
= 54000 × 7/100
= 378000/100
= $3780
Thus, Simple Interest = $3780
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 = $6000 + $3780
= $9780
Thus, Amount to be paid = $9780 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 = $6000
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 7 years
Thus, Amount (A)
= $6000 + ($6000 × 9% × 7)
= $6000 + ($6000 ×9/100 × 7)
= $6000 + (6000 × 9 × 7/100)
= $6000 + (54000 × 7/100)
= $6000 + (378000/100)
= $6000 + $3780 = $9780
Thus, Amount (A) to be paid = $9780 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 $6000, the simple interest in 1 year
= 9/100 × 6000
= 9 × 6000/100
= 54000/100 = $540
Thus, simple interest for 1 year = $540
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $540 × 7 = $3780
Thus, Simple Interest (SI) = $3780
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $3780
= $9780
Thus, Amount to be paid = $9780 Answer
Similar Questions
(1) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?
(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.
(3) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
(4) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
(5) How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?
(6) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 4 years.
(8) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(9) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
(10) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.