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) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?
(2) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 8 years.
(5) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(6) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(8) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?
(10) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.