Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.
Correct Answer
$3657
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 2%
Time (t) = 3 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% × 3
= $3450 ×2/100 × 3
= 3450 × 2 × 3/100
= 6900 × 3/100
= 20700/100
= $207
Thus, Simple Interest = $207
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 + $207
= $3657
Thus, Amount to be paid = $3657 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) = 3 years
Thus, Amount (A)
= $3450 + ($3450 × 2% × 3)
= $3450 + ($3450 ×2/100 × 3)
= $3450 + (3450 × 2 × 3/100)
= $3450 + (6900 × 3/100)
= $3450 + (20700/100)
= $3450 + $207 = $3657
Thus, Amount (A) to be paid = $3657 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 3 years
= Simple interest for 1 year × 3
= $69 × 3 = $207
Thus, Simple Interest (SI) = $207
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $207
= $3657
Thus, Amount to be paid = $3657 Answer
Similar Questions
(1) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(2) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.
(3) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(4) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) If Elizabeth paid $4002 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(7) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 10% simple interest?
(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.
(10) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.