Question:
Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
Correct Answer
$10165
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 9%
Time (t) = 10 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) = $5350 × 9% × 10
= $5350 ×9/100 × 10
= 5350 × 9 × 10/100
= 48150 × 10/100
= 481500/100
= $4815
Thus, Simple Interest = $4815
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 + $4815
= $10165
Thus, Amount to be paid = $10165 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5350 + ($5350 × 9% × 10)
= $5350 + ($5350 ×9/100 × 10)
= $5350 + (5350 × 9 × 10/100)
= $5350 + (48150 × 10/100)
= $5350 + (481500/100)
= $5350 + $4815 = $10165
Thus, Amount (A) to be paid = $10165 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 $5350, the simple interest in 1 year
= 9/100 × 5350
= 9 × 5350/100
= 48150/100 = $481.5
Thus, simple interest for 1 year = $481.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $481.5 × 10 = $4815
Thus, Simple Interest (SI) = $4815
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $4815
= $10165
Thus, Amount to be paid = $10165 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(2) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.
(3) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.
(5) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(6) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(7) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?
(8) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?
(10) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 10% simple interest?