Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.
Correct Answer
$6592
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 4%
Time (t) = 7 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) = $5150 × 4% × 7
= $5150 ×4/100 × 7
= 5150 × 4 × 7/100
= 20600 × 7/100
= 144200/100
= $1442
Thus, Simple Interest = $1442
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 = $5150 + $1442
= $6592
Thus, Amount to be paid = $6592 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 = $5150
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 7 years
Thus, Amount (A)
= $5150 + ($5150 × 4% × 7)
= $5150 + ($5150 ×4/100 × 7)
= $5150 + (5150 × 4 × 7/100)
= $5150 + (20600 × 7/100)
= $5150 + (144200/100)
= $5150 + $1442 = $6592
Thus, Amount (A) to be paid = $6592 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 $5150, the simple interest in 1 year
= 4/100 × 5150
= 4 × 5150/100
= 20600/100 = $206
Thus, simple interest for 1 year = $206
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $206 × 7 = $1442
Thus, Simple Interest (SI) = $1442
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1442
= $6592
Thus, Amount to be paid = $6592 Answer
Similar Questions
(1) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(2) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.
(4) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
(5) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 4 years.
(6) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(7) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?
(8) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?
(9) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.
(10) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 5% simple interest?