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) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 10% simple interest?
(2) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(3) In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?
(4) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 3 years.
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.
(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.
(7) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(8) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?
(10) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.