Question:
Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.
Correct Answer
$6050
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 3%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 7
= $5000 ×3/100 × 7
= 5000 × 3 × 7/100
= 15000 × 7/100
= 105000/100
= $1050
Thus, Simple Interest = $1050
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 + $1050
= $6050
Thus, Amount to be paid = $6050 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) = 3%
And, Time (t) = 7 years
Thus, Amount (A)
= $5000 + ($5000 × 3% × 7)
= $5000 + ($5000 ×3/100 × 7)
= $5000 + (5000 × 3 × 7/100)
= $5000 + (15000 × 7/100)
= $5000 + (105000/100)
= $5000 + $1050 = $6050
Thus, Amount (A) to be paid = $6050 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5000, the simple interest in 1 year
= 3/100 × 5000
= 3 × 5000/100
= 15000/100 = $150
Thus, simple interest for 1 year = $150
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $150 × 7 = $1050
Thus, Simple Interest (SI) = $1050
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $1050
= $6050
Thus, Amount to be paid = $6050 Answer
Similar Questions
(1) 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.
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.
(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 9% simple interest?
(4) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.
(6) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(7) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(8) If Sandra paid $4806 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 4% simple interest?