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) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?
(2) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 2% simple interest?
(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.
(4) If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?
(8) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(9) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.