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) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.
(2) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?
(3) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(4) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(5) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11946 to clear the loan, then find the time period of the loan.
(6) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 7 years.
(8) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(10) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.