Question:
Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
Correct Answer
$12000
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 10%
Time (t) = 10 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% × 10
= $6000 ×10/100 × 10
= 6000 × 10 × 10/100
= 60000 × 10/100
= 600000/100
= $6000
Thus, Simple Interest = $6000
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 + $6000
= $12000
Thus, Amount to be paid = $12000 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) = 10 years
Thus, Amount (A)
= $6000 + ($6000 × 10% × 10)
= $6000 + ($6000 ×10/100 × 10)
= $6000 + (6000 × 10 × 10/100)
= $6000 + (60000 × 10/100)
= $6000 + (600000/100)
= $6000 + $6000 = $12000
Thus, Amount (A) to be paid = $12000 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 10 years
= Simple interest for 1 year × 10
= $600 × 10 = $6000
Thus, Simple Interest (SI) = $6000
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $6000
= $12000
Thus, Amount to be paid = $12000 Answer
Similar Questions
(1) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.
(3) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10679 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 8 years.
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.
(6) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 8 years.
(8) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
(9) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(10) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?