Question:
What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?
Correct Answer
$3780
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 4%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 5
= $3150 ×4/100 × 5
= 3150 × 4 × 5/100
= 12600 × 5/100
= 63000/100
= $630
Thus, Simple Interest = $630
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 + $630
= $3780
Thus, Amount to be paid = $3780 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) = 4%
And, Time (t) = 5 years
Thus, Amount (A)
= $3150 + ($3150 × 4% × 5)
= $3150 + ($3150 ×4/100 × 5)
= $3150 + (3150 × 4 × 5/100)
= $3150 + (12600 × 5/100)
= $3150 + (63000/100)
= $3150 + $630 = $3780
Thus, Amount (A) to be paid = $3780 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3150, the simple interest in 1 year
= 4/100 × 3150
= 4 × 3150/100
= 12600/100 = $126
Thus, simple interest for 1 year = $126
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $126 × 5 = $630
Thus, Simple Interest (SI) = $630
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $630
= $3780
Thus, Amount to be paid = $3780 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.
(2) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 4 years.
(4) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(5) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8642 to clear the loan, then find the time period of the loan.
(6) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.
(8) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.