Question:
Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 6% simple interest.
Correct Answer
$7700
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 9
= $5000 ×6/100 × 9
= 5000 × 6 × 9/100
= 30000 × 9/100
= 270000/100
= $2700
Thus, Simple Interest = $2700
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 + $2700
= $7700
Thus, Amount to be paid = $7700 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) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5000 + ($5000 × 6% × 9)
= $5000 + ($5000 ×6/100 × 9)
= $5000 + (5000 × 6 × 9/100)
= $5000 + (30000 × 9/100)
= $5000 + (270000/100)
= $5000 + $2700 = $7700
Thus, Amount (A) to be paid = $7700 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5000, the simple interest in 1 year
= 6/100 × 5000
= 6 × 5000/100
= 30000/100 = $300
Thus, simple interest for 1 year = $300
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $300 × 9 = $2700
Thus, Simple Interest (SI) = $2700
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $2700
= $7700
Thus, Amount to be paid = $7700 Answer
Similar Questions
(1) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.
(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
(4) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(5) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.
(8) How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?
(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?
(10) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.