Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.
Correct Answer
$4032
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 7%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 4
= $3150 ×7/100 × 4
= 3150 × 7 × 4/100
= 22050 × 4/100
= 88200/100
= $882
Thus, Simple Interest = $882
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 + $882
= $4032
Thus, Amount to be paid = $4032 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) = 7%
And, Time (t) = 4 years
Thus, Amount (A)
= $3150 + ($3150 × 7% × 4)
= $3150 + ($3150 ×7/100 × 4)
= $3150 + (3150 × 7 × 4/100)
= $3150 + (22050 × 4/100)
= $3150 + (88200/100)
= $3150 + $882 = $4032
Thus, Amount (A) to be paid = $4032 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3150, the simple interest in 1 year
= 7/100 × 3150
= 7 × 3150/100
= 22050/100 = $220.5
Thus, simple interest for 1 year = $220.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $220.5 × 4 = $882
Thus, Simple Interest (SI) = $882
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $882
= $4032
Thus, Amount to be paid = $4032 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(2) How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?
(3) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?
(4) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?
(6) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 5% simple interest?
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.
(10) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.