Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
Correct Answer
$7068
Solution And Explanation
Solution
Given,
Principal (P) = $5700
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) = $5700 × 3% × 8
= $5700 ×3/100 × 8
= 5700 × 3 × 8/100
= 17100 × 8/100
= 136800/100
= $1368
Thus, Simple Interest = $1368
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 + $1368
= $7068
Thus, Amount to be paid = $7068 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5700 + ($5700 × 3% × 8)
= $5700 + ($5700 ×3/100 × 8)
= $5700 + (5700 × 3 × 8/100)
= $5700 + (17100 × 8/100)
= $5700 + (136800/100)
= $5700 + $1368 = $7068
Thus, Amount (A) to be paid = $7068 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 $5700, the simple interest in 1 year
= 3/100 × 5700
= 3 × 5700/100
= 17100/100 = $171
Thus, simple interest for 1 year = $171
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $171 × 8 = $1368
Thus, Simple Interest (SI) = $1368
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1368
= $7068
Thus, Amount to be paid = $7068 Answer
Similar Questions
(1) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 3 years.
(3) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.
(4) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 4 years.
(6) In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?
(7) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10679 to clear the loan, then find the time period of the loan.
(8) How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 8 years.