Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 7 years.
Correct Answer
$8791
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 7%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $5900 × 7% × 7
= $5900 ×7/100 × 7
= 5900 × 7 × 7/100
= 41300 × 7/100
= 289100/100
= $2891
Thus, Simple Interest = $2891
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 = $5900 + $2891
= $8791
Thus, Amount to be paid = $8791 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 = $5900
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5900 + ($5900 × 7% × 7)
= $5900 + ($5900 ×7/100 × 7)
= $5900 + (5900 × 7 × 7/100)
= $5900 + (41300 × 7/100)
= $5900 + (289100/100)
= $5900 + $2891 = $8791
Thus, Amount (A) to be paid = $8791 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5900, the simple interest in 1 year
= 7/100 × 5900
= 7 × 5900/100
= 41300/100 = $413
Thus, simple interest for 1 year = $413
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $413 × 7 = $2891
Thus, Simple Interest (SI) = $2891
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $2891
= $8791
Thus, Amount to be paid = $8791 Answer
Similar Questions
(1) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?
(2) How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?
(3) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?
(4) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?
(5) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
(6) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 9% simple interest?
(7) How much loan did Karen borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6842.5 to clear it?
(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?
(10) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8642 to clear the loan, then find the time period of the loan.