Question:
Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.
Correct Answer
$7080
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 2%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 9
= $6000 ×2/100 × 9
= 6000 × 2 × 9/100
= 12000 × 9/100
= 108000/100
= $1080
Thus, Simple Interest = $1080
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 + $1080
= $7080
Thus, Amount to be paid = $7080 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) = 2%
And, Time (t) = 9 years
Thus, Amount (A)
= $6000 + ($6000 × 2% × 9)
= $6000 + ($6000 ×2/100 × 9)
= $6000 + (6000 × 2 × 9/100)
= $6000 + (12000 × 9/100)
= $6000 + (108000/100)
= $6000 + $1080 = $7080
Thus, Amount (A) to be paid = $7080 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $6000, the simple interest in 1 year
= 2/100 × 6000
= 2 × 6000/100
= 12000/100 = $120
Thus, simple interest for 1 year = $120
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $120 × 9 = $1080
Thus, Simple Interest (SI) = $1080
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $1080
= $7080
Thus, Amount to be paid = $7080 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 7 years.
(4) How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?
(5) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 8% simple interest?
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 7 years.
(8) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.
(10) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.