Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 8 years.
Correct Answer
$8892
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5700 ×7/100 × 8
= 5700 × 7 × 8/100
= 39900 × 8/100
= 319200/100
= $3192
Thus, Simple Interest = $3192
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 + $3192
= $8892
Thus, Amount to be paid = $8892 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5700 + ($5700 × 7% × 8)
= $5700 + ($5700 ×7/100 × 8)
= $5700 + (5700 × 7 × 8/100)
= $5700 + (39900 × 8/100)
= $5700 + (319200/100)
= $5700 + $3192 = $8892
Thus, Amount (A) to be paid = $8892 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5700, the simple interest in 1 year
= 7/100 × 5700
= 7 × 5700/100
= 39900/100 = $399
Thus, simple interest for 1 year = $399
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $399 × 8 = $3192
Thus, Simple Interest (SI) = $3192
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $3192
= $8892
Thus, Amount to be paid = $8892 Answer
Similar Questions
(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 7 years.
(2) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.
(5) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(6) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 4 years.
(8) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?