Question:
Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 8 years.
Correct Answer
$10800
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 10%
Time (t) = 8 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% × 8
= $6000 ×10/100 × 8
= 6000 × 10 × 8/100
= 60000 × 8/100
= 480000/100
= $4800
Thus, Simple Interest = $4800
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 + $4800
= $10800
Thus, Amount to be paid = $10800 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) = 8 years
Thus, Amount (A)
= $6000 + ($6000 × 10% × 8)
= $6000 + ($6000 ×10/100 × 8)
= $6000 + (6000 × 10 × 8/100)
= $6000 + (60000 × 8/100)
= $6000 + (480000/100)
= $6000 + $4800 = $10800
Thus, Amount (A) to be paid = $10800 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 8 years
= Simple interest for 1 year × 8
= $600 × 8 = $4800
Thus, Simple Interest (SI) = $4800
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $4800
= $10800
Thus, Amount to be paid = $10800 Answer
Similar Questions
(1) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(2) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(3) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(4) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(5) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?
(6) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(7) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(10) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.