Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.
Correct Answer
$10620
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5900 ×10/100 × 8
= 5900 × 10 × 8/100
= 59000 × 8/100
= 472000/100
= $4720
Thus, Simple Interest = $4720
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 + $4720
= $10620
Thus, Amount to be paid = $10620 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5900 + ($5900 × 10% × 8)
= $5900 + ($5900 ×10/100 × 8)
= $5900 + (5900 × 10 × 8/100)
= $5900 + (59000 × 8/100)
= $5900 + (472000/100)
= $5900 + $4720 = $10620
Thus, Amount (A) to be paid = $10620 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5900, the simple interest in 1 year
= 10/100 × 5900
= 10 × 5900/100
= 59000/100 = $590
Thus, simple interest for 1 year = $590
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $590 × 8 = $4720
Thus, Simple Interest (SI) = $4720
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $4720
= $10620
Thus, Amount to be paid = $10620 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 4 years.
(3) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?
(4) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?
(5) If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 3 years.
(7) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(10) In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?