Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.
Correct Answer
$7313
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 6%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 7
= $5150 ×6/100 × 7
= 5150 × 6 × 7/100
= 30900 × 7/100
= 216300/100
= $2163
Thus, Simple Interest = $2163
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 + $2163
= $7313
Thus, Amount to be paid = $7313 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) = 6%
And, Time (t) = 7 years
Thus, Amount (A)
= $5150 + ($5150 × 6% × 7)
= $5150 + ($5150 ×6/100 × 7)
= $5150 + (5150 × 6 × 7/100)
= $5150 + (30900 × 7/100)
= $5150 + (216300/100)
= $5150 + $2163 = $7313
Thus, Amount (A) to be paid = $7313 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5150, the simple interest in 1 year
= 6/100 × 5150
= 6 × 5150/100
= 30900/100 = $309
Thus, simple interest for 1 year = $309
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $309 × 7 = $2163
Thus, Simple Interest (SI) = $2163
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2163
= $7313
Thus, Amount to be paid = $7313 Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 8 years.
(2) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(3) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(7) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.
(8) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.
(9) What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?
(10) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 6% simple interest?