Question:
If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$3276
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 2%
Time (t) = 2 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) = $3150 × 2% × 2
= $3150 ×2/100 × 2
= 3150 × 2 × 2/100
= 6300 × 2/100
= 12600/100
= $126
Thus, Simple Interest = $126
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 = $3150 + $126
= $3276
Thus, Amount to be paid = $3276 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 = $3150
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 2 years
Thus, Amount (A)
= $3150 + ($3150 × 2% × 2)
= $3150 + ($3150 ×2/100 × 2)
= $3150 + (3150 × 2 × 2/100)
= $3150 + (6300 × 2/100)
= $3150 + (12600/100)
= $3150 + $126 = $3276
Thus, Amount (A) to be paid = $3276 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 in 1 year = $2
∴ For $1, the simple interest in 1 year = 2/100
∴ For $3150, the simple interest in 1 year
= 2/100 × 3150
= 2 × 3150/100
= 6300/100 = $63
Thus, simple interest in 1 year = $63
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $63 × 2 = $126
Thus, Simple Interest (SI) = $126
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $126
= $3276
Thus, Amount to be paid = $3276 Answer
Similar Questions
(1) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?
(2) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(3) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.
(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.
(8) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.
(10) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.