Question:
Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
Correct Answer
$9000
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 8%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 10
= $5000 ×8/100 × 10
= 5000 × 8 × 10/100
= 40000 × 10/100
= 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) = 8%
And, Time (t) = 10 years
Thus, Amount (A)
= $5000 + ($5000 × 8% × 10)
= $5000 + ($5000 ×8/100 × 10)
= $5000 + (5000 × 8 × 10/100)
= $5000 + (40000 × 10/100)
= $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 = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5000, the simple interest in 1 year
= 8/100 × 5000
= 8 × 5000/100
= 40000/100 = $400
Thus, simple interest for 1 year = $400
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $400 × 10 = $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) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.
(2) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(4) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 7 years.
(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 2% simple interest?
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 3 years.
(7) Nancy had to pay $4772.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(10) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.