Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.
Correct Answer
$7630
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 5%
Time (t) = 8 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) = $5450 × 5% × 8
= $5450 ×5/100 × 8
= 5450 × 5 × 8/100
= 27250 × 8/100
= 218000/100
= $2180
Thus, Simple Interest = $2180
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 = $5450 + $2180
= $7630
Thus, Amount to be paid = $7630 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 = $5450
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5450 + ($5450 × 5% × 8)
= $5450 + ($5450 ×5/100 × 8)
= $5450 + (5450 × 5 × 8/100)
= $5450 + (27250 × 8/100)
= $5450 + (218000/100)
= $5450 + $2180 = $7630
Thus, Amount (A) to be paid = $7630 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 $5450, the simple interest in 1 year
= 5/100 × 5450
= 5 × 5450/100
= 27250/100 = $272.5
Thus, simple interest for 1 year = $272.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $272.5 × 8 = $2180
Thus, Simple Interest (SI) = $2180
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $2180
= $7630
Thus, Amount to be paid = $7630 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(2) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?
(3) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(4) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(5) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.
(7) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(8) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.