Question:
Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.
Correct Answer
$9000
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5000 ×10/100 × 8
= 5000 × 10 × 8/100
= 50000 × 8/100
= 400000/100
= $4000
Thus, Simple Interest = $4000
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 + $4000
= $9000
Thus, Amount to be paid = $9000 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5000 + ($5000 × 10% × 8)
= $5000 + ($5000 ×10/100 × 8)
= $5000 + (5000 × 10 × 8/100)
= $5000 + (50000 × 8/100)
= $5000 + (400000/100)
= $5000 + $4000 = $9000
Thus, Amount (A) to be paid = $9000 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5000, the simple interest in 1 year
= 10/100 × 5000
= 10 × 5000/100
= 50000/100 = $500
Thus, simple interest for 1 year = $500
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $500 × 8 = $4000
Thus, Simple Interest (SI) = $4000
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $4000
= $9000
Thus, Amount to be paid = $9000 Answer
Similar Questions
(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(2) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.
(3) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
(5) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.
(7) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(8) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 8 years.
(10) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?