Question:
Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 7 years.
Correct Answer
$6400
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 4%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5000 × 4% × 7
= $5000 ×4/100 × 7
= 5000 × 4 × 7/100
= 20000 × 7/100
= 140000/100
= $1400
Thus, Simple Interest = $1400
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 = $5000 + $1400
= $6400
Thus, Amount to be paid = $6400 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 = $5000
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 7 years
Thus, Amount (A)
= $5000 + ($5000 × 4% × 7)
= $5000 + ($5000 ×4/100 × 7)
= $5000 + (5000 × 4 × 7/100)
= $5000 + (20000 × 7/100)
= $5000 + (140000/100)
= $5000 + $1400 = $6400
Thus, Amount (A) to be paid = $6400 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5000, the simple interest in 1 year
= 4/100 × 5000
= 4 × 5000/100
= 20000/100 = $200
Thus, simple interest for 1 year = $200
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $200 × 7 = $1400
Thus, Simple Interest (SI) = $1400
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $1400
= $6400
Thus, Amount to be paid = $6400 Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?
(3) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(4) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.
(7) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 4 years.
(9) If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.