Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
Correct Answer
$8446
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 8
= $5150 ×8/100 × 8
= 5150 × 8 × 8/100
= 41200 × 8/100
= 329600/100
= $3296
Thus, Simple Interest = $3296
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 + $3296
= $8446
Thus, Amount to be paid = $8446 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) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 8% × 8)
= $5150 + ($5150 ×8/100 × 8)
= $5150 + (5150 × 8 × 8/100)
= $5150 + (41200 × 8/100)
= $5150 + (329600/100)
= $5150 + $3296 = $8446
Thus, Amount (A) to be paid = $8446 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5150, the simple interest in 1 year
= 8/100 × 5150
= 8 × 5150/100
= 41200/100 = $412
Thus, simple interest for 1 year = $412
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $412 × 8 = $3296
Thus, Simple Interest (SI) = $3296
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $3296
= $8446
Thus, Amount to be paid = $8446 Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.
(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 3 years.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.
(4) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(5) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.
(7) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(8) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(9) If Michael borrowed $3300 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.