Question:
Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
Correct Answer
$8265
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 5%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5700 × 5% × 9
= $5700 ×5/100 × 9
= 5700 × 5 × 9/100
= 28500 × 9/100
= 256500/100
= $2565
Thus, Simple Interest = $2565
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 = $5700 + $2565
= $8265
Thus, Amount to be paid = $8265 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 = $5700
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5700 + ($5700 × 5% × 9)
= $5700 + ($5700 ×5/100 × 9)
= $5700 + (5700 × 5 × 9/100)
= $5700 + (28500 × 9/100)
= $5700 + (256500/100)
= $5700 + $2565 = $8265
Thus, Amount (A) to be paid = $8265 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5700, the simple interest in 1 year
= 5/100 × 5700
= 5 × 5700/100
= 28500/100 = $285
Thus, simple interest for 1 year = $285
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $285 × 9 = $2565
Thus, Simple Interest (SI) = $2565
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $2565
= $8265
Thus, Amount to be paid = $8265 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(2) If Daniel paid $4756 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) If Daniel paid $4428 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.
(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.
(8) If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) If Paul paid $5640 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.