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) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.
(2) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?
(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.
(5) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
(7) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.
(9) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.