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) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?
(4) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.
(6) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(8) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
(9) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?