Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
Correct Answer
$7762.5
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 5%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5750 × 5% × 7
= $5750 ×5/100 × 7
= 5750 × 5 × 7/100
= 28750 × 7/100
= 201250/100
= $2012.5
Thus, Simple Interest = $2012.5
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 = $5750 + $2012.5
= $7762.5
Thus, Amount to be paid = $7762.5 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 = $5750
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5750 + ($5750 × 5% × 7)
= $5750 + ($5750 ×5/100 × 7)
= $5750 + (5750 × 5 × 7/100)
= $5750 + (28750 × 7/100)
= $5750 + (201250/100)
= $5750 + $2012.5 = $7762.5
Thus, Amount (A) to be paid = $7762.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5750, the simple interest in 1 year
= 5/100 × 5750
= 5 × 5750/100
= 28750/100 = $287.5
Thus, simple interest for 1 year = $287.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $287.5 × 7 = $2012.5
Thus, Simple Interest (SI) = $2012.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $2012.5
= $7762.5
Thus, Amount to be paid = $7762.5 Answer
Similar Questions
(1) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?
(2) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?
(4) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(5) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 3 years.
(7) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 7 years.
(9) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(10) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.