Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.
Correct Answer
$8755
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 10%
Time (t) = 7 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% × 7
= $5150 ×10/100 × 7
= 5150 × 10 × 7/100
= 51500 × 7/100
= 360500/100
= $3605
Thus, Simple Interest = $3605
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 + $3605
= $8755
Thus, Amount to be paid = $8755 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) = 7 years
Thus, Amount (A)
= $5150 + ($5150 × 10% × 7)
= $5150 + ($5150 ×10/100 × 7)
= $5150 + (5150 × 10 × 7/100)
= $5150 + (51500 × 7/100)
= $5150 + (360500/100)
= $5150 + $3605 = $8755
Thus, Amount (A) to be paid = $8755 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 7 years
= Simple interest for 1 year × 7
= $515 × 7 = $3605
Thus, Simple Interest (SI) = $3605
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $3605
= $8755
Thus, Amount to be paid = $8755 Answer
Similar Questions
(1) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
(2) If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.
(5) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.
(7) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(8) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Anthony had to pay $4816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.