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) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.
(3) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(4) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 3 years.
(6) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?
(8) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.
(9) If Jessica borrowed $3750 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.