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) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?
(2) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(3) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6258 to clear the loan, then find the time period of the loan.
(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?
(5) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.
(6) What amount will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?
(7) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) If Lisa paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.
(10) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.