Question:
Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.
Correct Answer
$4096
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (SI) = 7%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 4
= $3200 ×7/100 × 4
= 3200 × 7 × 4/100
= 22400 × 4/100
= 89600/100
= $896
Thus, Simple Interest = $896
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 + $896
= $4096
Thus, Amount to be paid = $4096 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) = 7%
And, Time (t) = 4 years
Thus, Amount (A)
= $3200 + ($3200 × 7% × 4)
= $3200 + ($3200 ×7/100 × 4)
= $3200 + (3200 × 7 × 4/100)
= $3200 + (22400 × 4/100)
= $3200 + (89600/100)
= $3200 + $896 = $4096
Thus, Amount (A) to be paid = $4096 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3200, the simple interest in 1 year
= 7/100 × 3200
= 7 × 3200/100
= 22400/100 = $224
Thus, simple interest for 1 year = $224
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $224 × 4 = $896
Thus, Simple Interest (SI) = $896
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3200 + $896
= $4096
Thus, Amount to be paid = $4096 Answer
Similar Questions
(1) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?
(2) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.
(4) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.
(6) Susan had to pay $4088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.
(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 10% simple interest?
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.