Question:
Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
Correct Answer
$11400
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 9
= $6000 ×10/100 × 9
= 6000 × 10 × 9/100
= 60000 × 9/100
= 540000/100
= $5400
Thus, Simple Interest = $5400
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 + $5400
= $11400
Thus, Amount to be paid = $11400 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) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $6000 + ($6000 × 10% × 9)
= $6000 + ($6000 ×10/100 × 9)
= $6000 + (6000 × 10 × 9/100)
= $6000 + (60000 × 9/100)
= $6000 + (540000/100)
= $6000 + $5400 = $11400
Thus, Amount (A) to be paid = $11400 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $6000, the simple interest in 1 year
= 10/100 × 6000
= 10 × 6000/100
= 60000/100 = $600
Thus, simple interest for 1 year = $600
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $600 × 9 = $5400
Thus, Simple Interest (SI) = $5400
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $5400
= $11400
Thus, Amount to be paid = $11400 Answer
Similar Questions
(1) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?
(2) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.
(4) Ashley had to pay $5232.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
(7) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.
(9) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?
(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 4 years.