Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.
Correct Answer
$7695
Solution And Explanation
Solution
Given,
Principal (P) = $5700
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) = $5700 × 5% × 7
= $5700 ×5/100 × 7
= 5700 × 5 × 7/100
= 28500 × 7/100
= 199500/100
= $1995
Thus, Simple Interest = $1995
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 + $1995
= $7695
Thus, Amount to be paid = $7695 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) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5700 + ($5700 × 5% × 7)
= $5700 + ($5700 ×5/100 × 7)
= $5700 + (5700 × 5 × 7/100)
= $5700 + (28500 × 7/100)
= $5700 + (199500/100)
= $5700 + $1995 = $7695
Thus, Amount (A) to be paid = $7695 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 $5700, the simple interest in 1 year
= 5/100 × 5700
= 5 × 5700/100
= 28500/100 = $285
Thus, simple interest for 1 year = $285
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $285 × 7 = $1995
Thus, Simple Interest (SI) = $1995
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1995
= $7695
Thus, Amount to be paid = $7695 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(2) If Mary borrowed $3050 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(3) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Donna had to pay $5141 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(6) How much loan did Margaret borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7937.5 to clear it?
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 3 years.
(8) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 3 years.
(10) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.