Question:
Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.
Correct Answer
$7020
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 5%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 7
= $5200 ×5/100 × 7
= 5200 × 5 × 7/100
= 26000 × 7/100
= 182000/100
= $1820
Thus, Simple Interest = $1820
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 + $1820
= $7020
Thus, Amount to be paid = $7020 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) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5200 + ($5200 × 5% × 7)
= $5200 + ($5200 ×5/100 × 7)
= $5200 + (5200 × 5 × 7/100)
= $5200 + (26000 × 7/100)
= $5200 + (182000/100)
= $5200 + $1820 = $7020
Thus, Amount (A) to be paid = $7020 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5200, the simple interest in 1 year
= 5/100 × 5200
= 5 × 5200/100
= 26000/100 = $260
Thus, simple interest for 1 year = $260
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $260 × 7 = $1820
Thus, Simple Interest (SI) = $1820
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $1820
= $7020
Thus, Amount to be paid = $7020 Answer
Similar Questions
(1) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?
(3) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 4 years.
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 4 years.
(8) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(10) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.