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) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.
(2) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(4) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7897 to clear the loan, then find the time period of the loan.
(5) How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?
(6) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(8) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.
(10) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 7 years.