Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.
Correct Answer
$8394.5
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 9%
Time (t) = 7 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) = $5150 × 9% × 7
= $5150 ×9/100 × 7
= 5150 × 9 × 7/100
= 46350 × 7/100
= 324450/100
= $3244.5
Thus, Simple Interest = $3244.5
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 + $3244.5
= $8394.5
Thus, Amount to be paid = $8394.5 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) = 9%
And, Time (t) = 7 years
Thus, Amount (A)
= $5150 + ($5150 × 9% × 7)
= $5150 + ($5150 ×9/100 × 7)
= $5150 + (5150 × 9 × 7/100)
= $5150 + (46350 × 7/100)
= $5150 + (324450/100)
= $5150 + $3244.5 = $8394.5
Thus, Amount (A) to be paid = $8394.5 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 $5150, the simple interest in 1 year
= 9/100 × 5150
= 9 × 5150/100
= 46350/100 = $463.5
Thus, simple interest for 1 year = $463.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $463.5 × 7 = $3244.5
Thus, Simple Interest (SI) = $3244.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $3244.5
= $8394.5
Thus, Amount to be paid = $8394.5 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 8 years.
(3) If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) If Karen borrowed $3950 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?
(6) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.
(7) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(8) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.
(9) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(10) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.