Question:
Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.
Correct Answer
$9630
Solution And Explanation
Solution
Given,
Principal (P) = $5350
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) = $5350 × 10% × 8
= $5350 ×10/100 × 8
= 5350 × 10 × 8/100
= 53500 × 8/100
= 428000/100
= $4280
Thus, Simple Interest = $4280
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 = $5350 + $4280
= $9630
Thus, Amount to be paid = $9630 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 = $5350
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5350 + ($5350 × 10% × 8)
= $5350 + ($5350 ×10/100 × 8)
= $5350 + (5350 × 10 × 8/100)
= $5350 + (53500 × 8/100)
= $5350 + (428000/100)
= $5350 + $4280 = $9630
Thus, Amount (A) to be paid = $9630 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 $5350, the simple interest in 1 year
= 10/100 × 5350
= 10 × 5350/100
= 53500/100 = $535
Thus, simple interest for 1 year = $535
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $535 × 8 = $4280
Thus, Simple Interest (SI) = $4280
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $4280
= $9630
Thus, Amount to be paid = $9630 Answer
Similar Questions
(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 3 years.
(3) If Donald paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(6) Betty had to pay $4632.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 3 years.
(8) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(9) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.