Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.
Correct Answer
$7194
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 8
= $5450 ×4/100 × 8
= 5450 × 4 × 8/100
= 21800 × 8/100
= 174400/100
= $1744
Thus, Simple Interest = $1744
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 + $1744
= $7194
Thus, Amount to be paid = $7194 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) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5450 + ($5450 × 4% × 8)
= $5450 + ($5450 ×4/100 × 8)
= $5450 + (5450 × 4 × 8/100)
= $5450 + (21800 × 8/100)
= $5450 + (174400/100)
= $5450 + $1744 = $7194
Thus, Amount (A) to be paid = $7194 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5450, the simple interest in 1 year
= 4/100 × 5450
= 4 × 5450/100
= 21800/100 = $218
Thus, simple interest for 1 year = $218
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $218 × 8 = $1744
Thus, Simple Interest (SI) = $1744
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $1744
= $7194
Thus, Amount to be paid = $7194 Answer
Similar Questions
(1) If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 3% simple interest?
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.
(5) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
(7) Joseph had to pay $4144 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 3 years.
(9) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 4 years.