Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.
Correct Answer
$7313
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 6%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 7
= $5150 ×6/100 × 7
= 5150 × 6 × 7/100
= 30900 × 7/100
= 216300/100
= $2163
Thus, Simple Interest = $2163
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 + $2163
= $7313
Thus, Amount to be paid = $7313 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) = 6%
And, Time (t) = 7 years
Thus, Amount (A)
= $5150 + ($5150 × 6% × 7)
= $5150 + ($5150 ×6/100 × 7)
= $5150 + (5150 × 6 × 7/100)
= $5150 + (30900 × 7/100)
= $5150 + (216300/100)
= $5150 + $2163 = $7313
Thus, Amount (A) to be paid = $7313 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5150, the simple interest in 1 year
= 6/100 × 5150
= 6 × 5150/100
= 30900/100 = $309
Thus, simple interest for 1 year = $309
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $309 × 7 = $2163
Thus, Simple Interest (SI) = $2163
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2163
= $7313
Thus, Amount to be paid = $7313 Answer
Similar Questions
(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.
(2) If Jennifer paid $3900 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?
(4) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?
(5) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(6) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 4 years.
(9) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(10) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.