Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
Correct Answer
$10300
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 10%
Time (t) = 10 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% × 10
= $5150 ×10/100 × 10
= 5150 × 10 × 10/100
= 51500 × 10/100
= 515000/100
= $5150
Thus, Simple Interest = $5150
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 + $5150
= $10300
Thus, Amount to be paid = $10300 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) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 10% × 10)
= $5150 + ($5150 ×10/100 × 10)
= $5150 + (5150 × 10 × 10/100)
= $5150 + (51500 × 10/100)
= $5150 + (515000/100)
= $5150 + $5150 = $10300
Thus, Amount (A) to be paid = $10300 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 10 years
= Simple interest for 1 year × 10
= $515 × 10 = $5150
Thus, Simple Interest (SI) = $5150
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $5150
= $10300
Thus, Amount to be paid = $10300 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(2) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?
(3) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(4) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(6) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 3 years.
(8) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?