Question:
Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
Correct Answer
$9000
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 5%
Time (t) = 10 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% × 10
= $6000 ×5/100 × 10
= 6000 × 5 × 10/100
= 30000 × 10/100
= 300000/100
= $3000
Thus, Simple Interest = $3000
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 + $3000
= $9000
Thus, Amount to be paid = $9000 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) = 10 years
Thus, Amount (A)
= $6000 + ($6000 × 5% × 10)
= $6000 + ($6000 ×5/100 × 10)
= $6000 + (6000 × 5 × 10/100)
= $6000 + (30000 × 10/100)
= $6000 + (300000/100)
= $6000 + $3000 = $9000
Thus, Amount (A) to be paid = $9000 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 10 years
= Simple interest for 1 year × 10
= $300 × 10 = $3000
Thus, Simple Interest (SI) = $3000
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $3000
= $9000
Thus, Amount to be paid = $9000 Answer
Similar Questions
(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 4 years.
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.
(4) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.
(7) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(8) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?
(10) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?