Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 7 years.
Correct Answer
$9010
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 10%
Time (t) = 7 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) = $5300 × 10% × 7
= $5300 ×10/100 × 7
= 5300 × 10 × 7/100
= 53000 × 7/100
= 371000/100
= $3710
Thus, Simple Interest = $3710
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 = $5300 + $3710
= $9010
Thus, Amount to be paid = $9010 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 = $5300
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 7 years
Thus, Amount (A)
= $5300 + ($5300 × 10% × 7)
= $5300 + ($5300 ×10/100 × 7)
= $5300 + (5300 × 10 × 7/100)
= $5300 + (53000 × 7/100)
= $5300 + (371000/100)
= $5300 + $3710 = $9010
Thus, Amount (A) to be paid = $9010 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 $5300, the simple interest in 1 year
= 10/100 × 5300
= 10 × 5300/100
= 53000/100 = $530
Thus, simple interest for 1 year = $530
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $530 × 7 = $3710
Thus, Simple Interest (SI) = $3710
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $3710
= $9010
Thus, Amount to be paid = $9010 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(3) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
(4) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 8 years.
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 8 years.
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 3 years.
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.
(9) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(10) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.