Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
Correct Answer
$8493
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 7%
Time (t) = 7 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% × 7
= $5700 ×7/100 × 7
= 5700 × 7 × 7/100
= 39900 × 7/100
= 279300/100
= $2793
Thus, Simple Interest = $2793
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 + $2793
= $8493
Thus, Amount to be paid = $8493 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) = 7 years
Thus, Amount (A)
= $5700 + ($5700 × 7% × 7)
= $5700 + ($5700 ×7/100 × 7)
= $5700 + (5700 × 7 × 7/100)
= $5700 + (39900 × 7/100)
= $5700 + (279300/100)
= $5700 + $2793 = $8493
Thus, Amount (A) to be paid = $8493 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 7 years
= Simple interest for 1 year × 7
= $399 × 7 = $2793
Thus, Simple Interest (SI) = $2793
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $2793
= $8493
Thus, Amount to be paid = $8493 Answer
Similar Questions
(1) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
(2) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 5% simple interest?
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.
(6) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(7) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.
(9) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?
(10) If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.