Question:
Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.
Correct Answer
$3712
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (SI) = 4%
Time (t) = 4 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) = $3200 × 4% × 4
= $3200 ×4/100 × 4
= 3200 × 4 × 4/100
= 12800 × 4/100
= 51200/100
= $512
Thus, Simple Interest = $512
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 + $512
= $3712
Thus, Amount to be paid = $3712 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) = 4%
And, Time (t) = 4 years
Thus, Amount (A)
= $3200 + ($3200 × 4% × 4)
= $3200 + ($3200 ×4/100 × 4)
= $3200 + (3200 × 4 × 4/100)
= $3200 + (12800 × 4/100)
= $3200 + (51200/100)
= $3200 + $512 = $3712
Thus, Amount (A) to be paid = $3712 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 $3200, the simple interest in 1 year
= 4/100 × 3200
= 4 × 3200/100
= 12800/100 = $128
Thus, simple interest for 1 year = $128
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $128 × 4 = $512
Thus, Simple Interest (SI) = $512
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3200 + $512
= $3712
Thus, Amount to be paid = $3712 Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.
(2) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(5) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
(7) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?
(8) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 3 years.
(10) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.