Question:
Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
Correct Answer
$9690
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 10%
Time (t) = 9 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) = $5100 × 10% × 9
= $5100 ×10/100 × 9
= 5100 × 10 × 9/100
= 51000 × 9/100
= 459000/100
= $4590
Thus, Simple Interest = $4590
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 + $4590
= $9690
Thus, Amount to be paid = $9690 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) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5100 + ($5100 × 10% × 9)
= $5100 + ($5100 ×10/100 × 9)
= $5100 + (5100 × 10 × 9/100)
= $5100 + (51000 × 9/100)
= $5100 + (459000/100)
= $5100 + $4590 = $9690
Thus, Amount (A) to be paid = $9690 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 $5100, the simple interest in 1 year
= 10/100 × 5100
= 10 × 5100/100
= 51000/100 = $510
Thus, simple interest for 1 year = $510
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $510 × 9 = $4590
Thus, Simple Interest (SI) = $4590
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $4590
= $9690
Thus, Amount to be paid = $9690 Answer
Similar Questions
(1) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
(6) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10168 to clear the loan, then find the time period of the loan.
(7) If Linda borrowed $3350 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.
(10) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.