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) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
(2) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
(3) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(4) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(5) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if David borrowed a sum of $3200 at a 6% simple interest?
(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.
(9) How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?
(10) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.