Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.
Correct Answer
$9265
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 10%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 7
= $5450 ×10/100 × 7
= 5450 × 10 × 7/100
= 54500 × 7/100
= 381500/100
= $3815
Thus, Simple Interest = $3815
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 + $3815
= $9265
Thus, Amount to be paid = $9265 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) = 10%
And, Time (t) = 7 years
Thus, Amount (A)
= $5450 + ($5450 × 10% × 7)
= $5450 + ($5450 ×10/100 × 7)
= $5450 + (5450 × 10 × 7/100)
= $5450 + (54500 × 7/100)
= $5450 + (381500/100)
= $5450 + $3815 = $9265
Thus, Amount (A) to be paid = $9265 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5450, the simple interest in 1 year
= 10/100 × 5450
= 10 × 5450/100
= 54500/100 = $545
Thus, simple interest for 1 year = $545
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $545 × 7 = $3815
Thus, Simple Interest (SI) = $3815
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $3815
= $9265
Thus, Amount to be paid = $9265 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(2) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.
(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?
(4) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.
(6) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(8) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.
(9) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.