Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.
Correct Answer
$6498
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 2%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $5700 × 2% × 7
= $5700 ×2/100 × 7
= 5700 × 2 × 7/100
= 11400 × 7/100
= 79800/100
= $798
Thus, Simple Interest = $798
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 = $5700 + $798
= $6498
Thus, Amount to be paid = $6498 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 = $5700
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 7 years
Thus, Amount (A)
= $5700 + ($5700 × 2% × 7)
= $5700 + ($5700 ×2/100 × 7)
= $5700 + (5700 × 2 × 7/100)
= $5700 + (11400 × 7/100)
= $5700 + (79800/100)
= $5700 + $798 = $6498
Thus, Amount (A) to be paid = $6498 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5700, the simple interest in 1 year
= 2/100 × 5700
= 2 × 5700/100
= 11400/100 = $114
Thus, simple interest for 1 year = $114
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $114 × 7 = $798
Thus, Simple Interest (SI) = $798
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $798
= $6498
Thus, Amount to be paid = $6498 Answer
Similar Questions
(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.
(2) 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.
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 8 years.
(4) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(5) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(6) What amount does David have to pay after 6 years if he takes a loan of $3400 at 6% simple interest?
(7) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.
(9) How much loan did Kevin borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8165 to clear it?
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.