Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.
Correct Answer
$8858
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 9%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 8
= $5150 ×9/100 × 8
= 5150 × 9 × 8/100
= 46350 × 8/100
= 370800/100
= $3708
Thus, Simple Interest = $3708
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 + $3708
= $8858
Thus, Amount to be paid = $8858 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) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 9% × 8)
= $5150 + ($5150 ×9/100 × 8)
= $5150 + (5150 × 9 × 8/100)
= $5150 + (46350 × 8/100)
= $5150 + (370800/100)
= $5150 + $3708 = $8858
Thus, Amount (A) to be paid = $8858 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5150, the simple interest in 1 year
= 9/100 × 5150
= 9 × 5150/100
= 46350/100 = $463.5
Thus, simple interest for 1 year = $463.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $463.5 × 8 = $3708
Thus, Simple Interest (SI) = $3708
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $3708
= $8858
Thus, Amount to be paid = $8858 Answer
Similar Questions
(1) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 4 years.
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.
(4) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(5) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(6) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?
(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.
(9) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.
(10) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.