Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.
Correct Answer
$3780
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 5%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 4
= $3150 ×5/100 × 4
= 3150 × 5 × 4/100
= 15750 × 4/100
= 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) = 5%
And, Time (t) = 4 years
Thus, Amount (A)
= $3150 + ($3150 × 5% × 4)
= $3150 + ($3150 ×5/100 × 4)
= $3150 + (3150 × 5 × 4/100)
= $3150 + (15750 × 4/100)
= $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 = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3150, the simple interest in 1 year
= 5/100 × 3150
= 5 × 3150/100
= 15750/100 = $157.5
Thus, simple interest for 1 year = $157.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $157.5 × 4 = $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) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(3) How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?
(4) Margaret had to pay $4872 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?
(7) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(9) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?
(10) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.