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) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8195 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 4 years.
(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(4) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?
(5) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?
(7) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 8 years.
(9) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?
(10) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.