Question:
Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.
Correct Answer
$7800
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5000 ×7/100 × 8
= 5000 × 7 × 8/100
= 35000 × 8/100
= 280000/100
= $2800
Thus, Simple Interest = $2800
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 + $2800
= $7800
Thus, Amount to be paid = $7800 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5000 + ($5000 × 7% × 8)
= $5000 + ($5000 ×7/100 × 8)
= $5000 + (5000 × 7 × 8/100)
= $5000 + (35000 × 8/100)
= $5000 + (280000/100)
= $5000 + $2800 = $7800
Thus, Amount (A) to be paid = $7800 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5000, the simple interest in 1 year
= 7/100 × 5000
= 7 × 5000/100
= 35000/100 = $350
Thus, simple interest for 1 year = $350
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $350 × 8 = $2800
Thus, Simple Interest (SI) = $2800
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $2800
= $7800
Thus, Amount to be paid = $7800 Answer
Similar Questions
(1) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(3) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.
(5) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?
(6) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(7) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
(8) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.
(10) If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.