Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.
Correct Answer
$3402
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 2%
Time (t) = 4 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% × 4
= $3150 ×2/100 × 4
= 3150 × 2 × 4/100
= 6300 × 4/100
= 25200/100
= $252
Thus, Simple Interest = $252
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 + $252
= $3402
Thus, Amount to be paid = $3402 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) = 4 years
Thus, Amount (A)
= $3150 + ($3150 × 2% × 4)
= $3150 + ($3150 ×2/100 × 4)
= $3150 + (3150 × 2 × 4/100)
= $3150 + (6300 × 4/100)
= $3150 + (25200/100)
= $3150 + $252 = $3402
Thus, Amount (A) to be paid = $3402 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 for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $3150, the simple interest in 1 year
= 2/100 × 3150
= 2 × 3150/100
= 6300/100 = $63
Thus, simple interest for 1 year = $63
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $63 × 4 = $252
Thus, Simple Interest (SI) = $252
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $252
= $3402
Thus, Amount to be paid = $3402 Answer
Similar Questions
(1) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.
(3) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
(5) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.
(7) How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.
(9) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.
(10) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.