Question:
Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 3 years.
Correct Answer
$4572
Solution And Explanation
Solution
Given,
Principal (P) = $3600
Rate of Simple Interest (SI) = 9%
Time (t) = 3 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) = $3600 × 9% × 3
= $3600 ×9/100 × 3
= 3600 × 9 × 3/100
= 32400 × 3/100
= 97200/100
= $972
Thus, Simple Interest = $972
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 = $3600 + $972
= $4572
Thus, Amount to be paid = $4572 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 = $3600
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 3 years
Thus, Amount (A)
= $3600 + ($3600 × 9% × 3)
= $3600 + ($3600 ×9/100 × 3)
= $3600 + (3600 × 9 × 3/100)
= $3600 + (32400 × 3/100)
= $3600 + (97200/100)
= $3600 + $972 = $4572
Thus, Amount (A) to be paid = $4572 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 $3600, the simple interest in 1 year
= 9/100 × 3600
= 9 × 3600/100
= 32400/100 = $324
Thus, simple interest for 1 year = $324
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $324 × 3 = $972
Thus, Simple Interest (SI) = $972
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3600 + $972
= $4572
Thus, Amount to be paid = $4572 Answer
Similar Questions
(1) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(2) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(3) How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?
(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
(5) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(6) Mark had to pay $4928 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?
(8) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?
(10) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.