Question:
Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 4 years.
Correct Answer
$3840
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (SI) = 5%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $3200 × 5% × 4
= $3200 ×5/100 × 4
= 3200 × 5 × 4/100
= 16000 × 4/100
= 64000/100
= $640
Thus, Simple Interest = $640
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 = $3200 + $640
= $3840
Thus, Amount to be paid = $3840 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 = $3200
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 4 years
Thus, Amount (A)
= $3200 + ($3200 × 5% × 4)
= $3200 + ($3200 ×5/100 × 4)
= $3200 + (3200 × 5 × 4/100)
= $3200 + (16000 × 4/100)
= $3200 + (64000/100)
= $3200 + $640 = $3840
Thus, Amount (A) to be paid = $3840 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3200, the simple interest in 1 year
= 5/100 × 3200
= 5 × 3200/100
= 16000/100 = $160
Thus, simple interest for 1 year = $160
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $160 × 4 = $640
Thus, Simple Interest (SI) = $640
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3200 + $640
= $3840
Thus, Amount to be paid = $3840 Answer
Similar Questions
(1) How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?
(2) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if James borrowed a sum of $3000 at a 7% simple interest?
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.
(5) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 7 years.
(7) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.
(9) If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7421 to clear the loan, then find the time period of the loan.