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) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(2) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?
(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(4) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(6) If Sandra paid $4806 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.
(8) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(9) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?
(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?