Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.
Correct Answer
$9617
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 9%
Time (t) = 7 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) = $5900 × 9% × 7
= $5900 ×9/100 × 7
= 5900 × 9 × 7/100
= 53100 × 7/100
= 371700/100
= $3717
Thus, Simple Interest = $3717
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 + $3717
= $9617
Thus, Amount to be paid = $9617 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) = 9%
And, Time (t) = 7 years
Thus, Amount (A)
= $5900 + ($5900 × 9% × 7)
= $5900 + ($5900 ×9/100 × 7)
= $5900 + (5900 × 9 × 7/100)
= $5900 + (53100 × 7/100)
= $5900 + (371700/100)
= $5900 + $3717 = $9617
Thus, Amount (A) to be paid = $9617 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 $5900, the simple interest in 1 year
= 9/100 × 5900
= 9 × 5900/100
= 53100/100 = $531
Thus, simple interest for 1 year = $531
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $531 × 7 = $3717
Thus, Simple Interest (SI) = $3717
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $3717
= $9617
Thus, Amount to be paid = $9617 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5712 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.
(3) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.
(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?
(6) Anthony had to pay $4816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?
(8) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?
(9) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.
(10) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.