Question:
Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.
Correct Answer
$7000
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 8
= $5000 ×5/100 × 8
= 5000 × 5 × 8/100
= 25000 × 8/100
= 200000/100
= $2000
Thus, Simple Interest = $2000
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 + $2000
= $7000
Thus, Amount to be paid = $7000 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) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5000 + ($5000 × 5% × 8)
= $5000 + ($5000 ×5/100 × 8)
= $5000 + (5000 × 5 × 8/100)
= $5000 + (25000 × 8/100)
= $5000 + (200000/100)
= $5000 + $2000 = $7000
Thus, Amount (A) to be paid = $7000 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5000, the simple interest in 1 year
= 5/100 × 5000
= 5 × 5000/100
= 25000/100 = $250
Thus, simple interest for 1 year = $250
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $250 × 8 = $2000
Thus, Simple Interest (SI) = $2000
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $2000
= $7000
Thus, Amount to be paid = $7000 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(2) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?
(3) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.
(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?
(7) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.
(9) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(10) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.