Question:
Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.
Correct Answer
$8840
Solution And Explanation
Solution
Given,
Principal (P) = $5200
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) = $5200 × 10% × 7
= $5200 ×10/100 × 7
= 5200 × 10 × 7/100
= 52000 × 7/100
= 364000/100
= $3640
Thus, Simple Interest = $3640
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 = $5200 + $3640
= $8840
Thus, Amount to be paid = $8840 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 = $5200
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 7 years
Thus, Amount (A)
= $5200 + ($5200 × 10% × 7)
= $5200 + ($5200 ×10/100 × 7)
= $5200 + (5200 × 10 × 7/100)
= $5200 + (52000 × 7/100)
= $5200 + (364000/100)
= $5200 + $3640 = $8840
Thus, Amount (A) to be paid = $8840 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 $5200, the simple interest in 1 year
= 10/100 × 5200
= 10 × 5200/100
= 52000/100 = $520
Thus, simple interest for 1 year = $520
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $520 × 7 = $3640
Thus, Simple Interest (SI) = $3640
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $3640
= $8840
Thus, Amount to be paid = $8840 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.
(2) 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.
(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
(5) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(6) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?
(7) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.
(9) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?