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 John borrowed a sum of $5200 at 4% simple interest for 8 years.
(2) How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?
(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 10% simple interest?
(4) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 3 years.
(5) In how much time a principal of $3000 will amount to $3300 at a simple interest of 2% per annum?
(6) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 7 years.
(7) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.
(9) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.
(10) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?