Question:
Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.
Correct Answer
$8639
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 7%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 9
= $5300 ×7/100 × 9
= 5300 × 7 × 9/100
= 37100 × 9/100
= 333900/100
= $3339
Thus, Simple Interest = $3339
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 + $3339
= $8639
Thus, Amount to be paid = $8639 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) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5300 + ($5300 × 7% × 9)
= $5300 + ($5300 ×7/100 × 9)
= $5300 + (5300 × 7 × 9/100)
= $5300 + (37100 × 9/100)
= $5300 + (333900/100)
= $5300 + $3339 = $8639
Thus, Amount (A) to be paid = $8639 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5300, the simple interest in 1 year
= 7/100 × 5300
= 7 × 5300/100
= 37100/100 = $371
Thus, simple interest for 1 year = $371
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $371 × 9 = $3339
Thus, Simple Interest (SI) = $3339
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $3339
= $8639
Thus, Amount to be paid = $8639 Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.
(2) How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?
(3) Christopher took a loan of $6000 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.
(4) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(5) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 4 years.
(7) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.
(9) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 7 years.