Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 7 years.
Correct Answer
$9291
Solution And Explanation
Solution
Given,
Principal (P) = $5700
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) = $5700 × 9% × 7
= $5700 ×9/100 × 7
= 5700 × 9 × 7/100
= 51300 × 7/100
= 359100/100
= $3591
Thus, Simple Interest = $3591
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 = $5700 + $3591
= $9291
Thus, Amount to be paid = $9291 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 = $5700
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 7 years
Thus, Amount (A)
= $5700 + ($5700 × 9% × 7)
= $5700 + ($5700 ×9/100 × 7)
= $5700 + (5700 × 9 × 7/100)
= $5700 + (51300 × 7/100)
= $5700 + (359100/100)
= $5700 + $3591 = $9291
Thus, Amount (A) to be paid = $9291 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 $5700, the simple interest in 1 year
= 9/100 × 5700
= 9 × 5700/100
= 51300/100 = $513
Thus, simple interest for 1 year = $513
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $513 × 7 = $3591
Thus, Simple Interest (SI) = $3591
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $3591
= $9291
Thus, Amount to be paid = $9291 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 $7790 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 9% simple interest?
(3) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?
(4) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.
(5) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.
(6) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 to clear the loan, then find the time period of the loan.
(7) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?
(9) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.