Question:
Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
Correct Answer
$7493
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 3%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $5900 × 3% × 9
= $5900 ×3/100 × 9
= 5900 × 3 × 9/100
= 17700 × 9/100
= 159300/100
= $1593
Thus, Simple Interest = $1593
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 = $5900 + $1593
= $7493
Thus, Amount to be paid = $7493 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 = $5900
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5900 + ($5900 × 3% × 9)
= $5900 + ($5900 ×3/100 × 9)
= $5900 + (5900 × 3 × 9/100)
= $5900 + (17700 × 9/100)
= $5900 + (159300/100)
= $5900 + $1593 = $7493
Thus, Amount (A) to be paid = $7493 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5900, the simple interest in 1 year
= 3/100 × 5900
= 3 × 5900/100
= 17700/100 = $177
Thus, simple interest for 1 year = $177
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $177 × 9 = $1593
Thus, Simple Interest (SI) = $1593
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $1593
= $7493
Thus, Amount to be paid = $7493 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.
(3) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(5) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(7) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.
(9) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?
(10) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.