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) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8195 to clear the loan, then find the time period of the loan.
(2) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.
(4) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?
(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.
(7) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(8) If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?
(10) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?