Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.
Correct Answer
$10620
Solution And Explanation
Solution
Given,
Principal (P) = $5900
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) = $5900 × 10% × 8
= $5900 ×10/100 × 8
= 5900 × 10 × 8/100
= 59000 × 8/100
= 472000/100
= $4720
Thus, Simple Interest = $4720
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 = $5900 + $4720
= $10620
Thus, Amount to be paid = $10620 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 = $5900
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5900 + ($5900 × 10% × 8)
= $5900 + ($5900 ×10/100 × 8)
= $5900 + (5900 × 10 × 8/100)
= $5900 + (59000 × 8/100)
= $5900 + (472000/100)
= $5900 + $4720 = $10620
Thus, Amount (A) to be paid = $10620 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 $5900, the simple interest in 1 year
= 10/100 × 5900
= 10 × 5900/100
= 59000/100 = $590
Thus, simple interest for 1 year = $590
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $590 × 8 = $4720
Thus, Simple Interest (SI) = $4720
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $4720
= $10620
Thus, Amount to be paid = $10620 Answer
Similar Questions
(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 7 years.
(3) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(4) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.
(5) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(6) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 7 years.
(8) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 4 years.
(10) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.