Question:
Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.
Correct Answer
$6600
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5000 × 4% × 8
= $5000 ×4/100 × 8
= 5000 × 4 × 8/100
= 20000 × 8/100
= 160000/100
= $1600
Thus, Simple Interest = $1600
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 = $5000 + $1600
= $6600
Thus, Amount to be paid = $6600 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 = $5000
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5000 + ($5000 × 4% × 8)
= $5000 + ($5000 ×4/100 × 8)
= $5000 + (5000 × 4 × 8/100)
= $5000 + (20000 × 8/100)
= $5000 + (160000/100)
= $5000 + $1600 = $6600
Thus, Amount (A) to be paid = $6600 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5000, the simple interest in 1 year
= 4/100 × 5000
= 4 × 5000/100
= 20000/100 = $200
Thus, simple interest for 1 year = $200
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $200 × 8 = $1600
Thus, Simple Interest (SI) = $1600
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $1600
= $6600
Thus, Amount to be paid = $6600 Answer
Similar Questions
(1) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?
(3) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?
(4) How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?
(5) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.
(6) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 3 years.
(8) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?
(9) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.