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) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10679 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(3) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 4 years.
(4) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(5) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?
(6) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?
(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(9) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 3 years.