Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.
Correct Answer
$9690
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 10%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 7
= $5700 ×10/100 × 7
= 5700 × 10 × 7/100
= 57000 × 7/100
= 399000/100
= $3990
Thus, Simple Interest = $3990
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 + $3990
= $9690
Thus, Amount to be paid = $9690 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) = 10%
And, Time (t) = 7 years
Thus, Amount (A)
= $5700 + ($5700 × 10% × 7)
= $5700 + ($5700 ×10/100 × 7)
= $5700 + (5700 × 10 × 7/100)
= $5700 + (57000 × 7/100)
= $5700 + (399000/100)
= $5700 + $3990 = $9690
Thus, Amount (A) to be paid = $9690 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5700, the simple interest in 1 year
= 10/100 × 5700
= 10 × 5700/100
= 57000/100 = $570
Thus, simple interest for 1 year = $570
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $570 × 7 = $3990
Thus, Simple Interest (SI) = $3990
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $3990
= $9690
Thus, Amount to be paid = $9690 Answer
Similar Questions
(1) How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?
(2) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 3 years.
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.
(5) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(6) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?
(7) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 4 years.