Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
Correct Answer
$9270
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5150 ×10/100 × 8
= 5150 × 10 × 8/100
= 51500 × 8/100
= 412000/100
= $4120
Thus, Simple Interest = $4120
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 + $4120
= $9270
Thus, Amount to be paid = $9270 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 10% × 8)
= $5150 + ($5150 ×10/100 × 8)
= $5150 + (5150 × 10 × 8/100)
= $5150 + (51500 × 8/100)
= $5150 + (412000/100)
= $5150 + $4120 = $9270
Thus, Amount (A) to be paid = $9270 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5150, the simple interest in 1 year
= 10/100 × 5150
= 10 × 5150/100
= 51500/100 = $515
Thus, simple interest for 1 year = $515
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $515 × 8 = $4120
Thus, Simple Interest (SI) = $4120
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $4120
= $9270
Thus, Amount to be paid = $9270 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(2) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.
(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(4) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.
(6) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.
(8) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Barbara had to pay $4082.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 5% simple interest?