Question:
Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.
Correct Answer
$6413.5
Solution And Explanation
Solution
Given,
Principal (P) = $5050
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) = $5050 × 3% × 9
= $5050 ×3/100 × 9
= 5050 × 3 × 9/100
= 15150 × 9/100
= 136350/100
= $1363.5
Thus, Simple Interest = $1363.5
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 = $5050 + $1363.5
= $6413.5
Thus, Amount to be paid = $6413.5 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 = $5050
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5050 + ($5050 × 3% × 9)
= $5050 + ($5050 ×3/100 × 9)
= $5050 + (5050 × 3 × 9/100)
= $5050 + (15150 × 9/100)
= $5050 + (136350/100)
= $5050 + $1363.5 = $6413.5
Thus, Amount (A) to be paid = $6413.5 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 $5050, the simple interest in 1 year
= 3/100 × 5050
= 3 × 5050/100
= 15150/100 = $151.5
Thus, simple interest for 1 year = $151.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $151.5 × 9 = $1363.5
Thus, Simple Interest (SI) = $1363.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $1363.5
= $6413.5
Thus, Amount to be paid = $6413.5 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(2) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(4) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.
(5) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?
(7) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.
(8) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(9) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?