Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.
Correct Answer
$7357.5
Solution And Explanation
Solution
Given,
Principal (P) = $5450
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) = $5450 × 5% × 7
= $5450 ×5/100 × 7
= 5450 × 5 × 7/100
= 27250 × 7/100
= 190750/100
= $1907.5
Thus, Simple Interest = $1907.5
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 = $5450 + $1907.5
= $7357.5
Thus, Amount to be paid = $7357.5 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 = $5450
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5450 + ($5450 × 5% × 7)
= $5450 + ($5450 ×5/100 × 7)
= $5450 + (5450 × 5 × 7/100)
= $5450 + (27250 × 7/100)
= $5450 + (190750/100)
= $5450 + $1907.5 = $7357.5
Thus, Amount (A) to be paid = $7357.5 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 $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 7 years
= Simple interest for 1 year × 7
= $272.5 × 7 = $1907.5
Thus, Simple Interest (SI) = $1907.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $1907.5
= $7357.5
Thus, Amount to be paid = $7357.5 Answer
Similar Questions
(1) Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(3) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.
(4) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?
(5) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?
(6) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 4 years.
(9) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?
(10) Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.