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) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?
(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(3) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.
(5) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.
(7) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10168 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(9) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(10) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?