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) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 4 years.
(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?
(3) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 8% simple interest?
(5) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.
(7) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.
(9) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(10) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?