Question:
What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?
Correct Answer
$4252.5
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 7%
Time (t) = 5 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% × 5
= $3150 ×7/100 × 5
= 3150 × 7 × 5/100
= 22050 × 5/100
= 110250/100
= $1102.5
Thus, Simple Interest = $1102.5
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 + $1102.5
= $4252.5
Thus, Amount to be paid = $4252.5 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) = 5 years
Thus, Amount (A)
= $3150 + ($3150 × 7% × 5)
= $3150 + ($3150 ×7/100 × 5)
= $3150 + (3150 × 7 × 5/100)
= $3150 + (22050 × 5/100)
= $3150 + (110250/100)
= $3150 + $1102.5 = $4252.5
Thus, Amount (A) to be paid = $4252.5 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 5 years
= Simple interest for 1 year × 5
= $220.5 × 5 = $1102.5
Thus, Simple Interest (SI) = $1102.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $1102.5
= $4252.5
Thus, Amount to be paid = $4252.5 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) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
(3) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.
(5) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 4 years.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.
(7) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?
(8) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 3 years.
(10) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.