Question:
If Elizabeth borrowed $3450 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$3657
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 3%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 2
= $3450 ×3/100 × 2
= 3450 × 3 × 2/100
= 10350 × 2/100
= 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) = 3%
And, Time (t) = 2 years
Thus, Amount (A)
= $3450 + ($3450 × 3% × 2)
= $3450 + ($3450 ×3/100 × 2)
= $3450 + (3450 × 3 × 2/100)
= $3450 + (10350 × 2/100)
= $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 = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3450, the simple interest in 1 year
= 3/100 × 3450
= 3 × 3450/100
= 10350/100 = $103.5
Thus, simple interest for 1 year = $103.5
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $103.5 × 2 = $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) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 4 years.
(3) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.
(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?
(6) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(7) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
(9) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(10) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.