Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
Correct Answer
$3726
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 2%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $3450 × 2% × 4
= $3450 ×2/100 × 4
= 3450 × 2 × 4/100
= 6900 × 4/100
= 27600/100
= $276
Thus, Simple Interest = $276
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 = $3450 + $276
= $3726
Thus, Amount to be paid = $3726 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 = $3450
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 4 years
Thus, Amount (A)
= $3450 + ($3450 × 2% × 4)
= $3450 + ($3450 ×2/100 × 4)
= $3450 + (3450 × 2 × 4/100)
= $3450 + (6900 × 4/100)
= $3450 + (27600/100)
= $3450 + $276 = $3726
Thus, Amount (A) to be paid = $3726 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $3450, the simple interest in 1 year
= 2/100 × 3450
= 2 × 3450/100
= 6900/100 = $69
Thus, simple interest for 1 year = $69
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $69 × 4 = $276
Thus, Simple Interest (SI) = $276
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $276
= $3726
Thus, Amount to be paid = $3726 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 3 years.
(3) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(4) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 3 years.
(6) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 7 years.
(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) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(10) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.