Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.
Correct Answer
$6758
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5450 ×3/100 × 8
= 5450 × 3 × 8/100
= 16350 × 8/100
= 130800/100
= $1308
Thus, Simple Interest = $1308
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 + $1308
= $6758
Thus, Amount to be paid = $6758 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5450 + ($5450 × 3% × 8)
= $5450 + ($5450 ×3/100 × 8)
= $5450 + (5450 × 3 × 8/100)
= $5450 + (16350 × 8/100)
= $5450 + (130800/100)
= $5450 + $1308 = $6758
Thus, Amount (A) to be paid = $6758 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5450, the simple interest in 1 year
= 3/100 × 5450
= 3 × 5450/100
= 16350/100 = $163.5
Thus, simple interest for 1 year = $163.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $163.5 × 8 = $1308
Thus, Simple Interest (SI) = $1308
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $1308
= $6758
Thus, Amount to be paid = $6758 Answer
Similar Questions
(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.
(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(3) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(4) Mark had to pay $4664 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.
(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?
(8) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.
(10) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.