Question:
Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
Correct Answer
$9690
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10
= $5100 ×9/100 × 10
= 5100 × 9 × 10/100
= 45900 × 10/100
= 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5100 + ($5100 × 9% × 10)
= $5100 + ($5100 ×9/100 × 10)
= $5100 + (5100 × 9 × 10/100)
= $5100 + (45900 × 10/100)
= $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 = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5100, the simple interest in 1 year
= 9/100 × 5100
= 9 × 5100/100
= 45900/100 = $459
Thus, simple interest for 1 year = $459
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $459 × 10 = $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) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(2) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(3) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(4) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.
(6) How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?
(7) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.
(9) How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?
(10) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?