Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
Correct Answer
$8313
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 9%
Time (t) = 7 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% × 7
= $5100 ×9/100 × 7
= 5100 × 9 × 7/100
= 45900 × 7/100
= 321300/100
= $3213
Thus, Simple Interest = $3213
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 + $3213
= $8313
Thus, Amount to be paid = $8313 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) = 7 years
Thus, Amount (A)
= $5100 + ($5100 × 9% × 7)
= $5100 + ($5100 ×9/100 × 7)
= $5100 + (5100 × 9 × 7/100)
= $5100 + (45900 × 7/100)
= $5100 + (321300/100)
= $5100 + $3213 = $8313
Thus, Amount (A) to be paid = $8313 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 7 years
= Simple interest for 1 year × 7
= $459 × 7 = $3213
Thus, Simple Interest (SI) = $3213
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $3213
= $8313
Thus, Amount to be paid = $8313 Answer
Similar Questions
(1) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?
(2) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(3) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.
(6) If Jennifer paid $3510 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?
(8) John had to pay $3488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.