Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
Correct Answer
$7673.5
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 7%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 7
= $5150 ×7/100 × 7
= 5150 × 7 × 7/100
= 36050 × 7/100
= 252350/100
= $2523.5
Thus, Simple Interest = $2523.5
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 + $2523.5
= $7673.5
Thus, Amount to be paid = $7673.5 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) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5150 + ($5150 × 7% × 7)
= $5150 + ($5150 ×7/100 × 7)
= $5150 + (5150 × 7 × 7/100)
= $5150 + (36050 × 7/100)
= $5150 + (252350/100)
= $5150 + $2523.5 = $7673.5
Thus, Amount (A) to be paid = $7673.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5150, the simple interest in 1 year
= 7/100 × 5150
= 7 × 5150/100
= 36050/100 = $360.5
Thus, simple interest for 1 year = $360.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $360.5 × 7 = $2523.5
Thus, Simple Interest (SI) = $2523.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2523.5
= $7673.5
Thus, Amount to be paid = $7673.5 Answer
Similar Questions
(1) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 8 years.
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.
(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.
(4) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(5) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 7 years.
(7) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?
(8) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?
(9) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?