Question:
Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
Correct Answer
$8700
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 5%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 9
= $6000 ×5/100 × 9
= 6000 × 5 × 9/100
= 30000 × 9/100
= 270000/100
= $2700
Thus, Simple Interest = $2700
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 + $2700
= $8700
Thus, Amount to be paid = $8700 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) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $6000 + ($6000 × 5% × 9)
= $6000 + ($6000 ×5/100 × 9)
= $6000 + (6000 × 5 × 9/100)
= $6000 + (30000 × 9/100)
= $6000 + (270000/100)
= $6000 + $2700 = $8700
Thus, Amount (A) to be paid = $8700 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $6000, the simple interest in 1 year
= 5/100 × 6000
= 5 × 6000/100
= 30000/100 = $300
Thus, simple interest for 1 year = $300
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $300 × 9 = $2700
Thus, Simple Interest (SI) = $2700
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $2700
= $8700
Thus, Amount to be paid = $8700 Answer
Similar Questions
(1) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?
(2) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(3) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?
(4) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 4 years.
(6) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(8) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8344 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 8 years.
(10) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.