Question:
Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
Correct Answer
$7854
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5100 × 6% × 9
= $5100 ×6/100 × 9
= 5100 × 6 × 9/100
= 30600 × 9/100
= 275400/100
= $2754
Thus, Simple Interest = $2754
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 = $5100 + $2754
= $7854
Thus, Amount to be paid = $7854 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 = $5100
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5100 + ($5100 × 6% × 9)
= $5100 + ($5100 ×6/100 × 9)
= $5100 + (5100 × 6 × 9/100)
= $5100 + (30600 × 9/100)
= $5100 + (275400/100)
= $5100 + $2754 = $7854
Thus, Amount (A) to be paid = $7854 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5100, the simple interest in 1 year
= 6/100 × 5100
= 6 × 5100/100
= 30600/100 = $306
Thus, simple interest for 1 year = $306
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $306 × 9 = $2754
Thus, Simple Interest (SI) = $2754
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $2754
= $7854
Thus, Amount to be paid = $7854 Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.
(2) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(3) How much loan did Kevin borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8165 to clear it?
(4) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(5) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(7) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(8) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.
(10) If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.