Question:
Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 8 years.
Correct Answer
$8600
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 9%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 8
= $5000 ×9/100 × 8
= 5000 × 9 × 8/100
= 45000 × 8/100
= 360000/100
= $3600
Thus, Simple Interest = $3600
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 + $3600
= $8600
Thus, Amount to be paid = $8600 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) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5000 + ($5000 × 9% × 8)
= $5000 + ($5000 ×9/100 × 8)
= $5000 + (5000 × 9 × 8/100)
= $5000 + (45000 × 8/100)
= $5000 + (360000/100)
= $5000 + $3600 = $8600
Thus, Amount (A) to be paid = $8600 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5000, the simple interest in 1 year
= 9/100 × 5000
= 9 × 5000/100
= 45000/100 = $450
Thus, simple interest for 1 year = $450
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $450 × 8 = $3600
Thus, Simple Interest (SI) = $3600
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $3600
= $8600
Thus, Amount to be paid = $8600 Answer
Similar Questions
(1) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(2) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(4) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.
(5) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) 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.
(7) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(8) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?
(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 10% simple interest?
(10) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 4% simple interest?