Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.
Correct Answer
$7897
Solution And Explanation
Solution
Given,
Principal (P) = $5300
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) = $5300 × 7% × 7
= $5300 ×7/100 × 7
= 5300 × 7 × 7/100
= 37100 × 7/100
= 259700/100
= $2597
Thus, Simple Interest = $2597
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 = $5300 + $2597
= $7897
Thus, Amount to be paid = $7897 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 = $5300
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5300 + ($5300 × 7% × 7)
= $5300 + ($5300 ×7/100 × 7)
= $5300 + (5300 × 7 × 7/100)
= $5300 + (37100 × 7/100)
= $5300 + (259700/100)
= $5300 + $2597 = $7897
Thus, Amount (A) to be paid = $7897 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 $5300, the simple interest in 1 year
= 7/100 × 5300
= 7 × 5300/100
= 37100/100 = $371
Thus, simple interest for 1 year = $371
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $371 × 7 = $2597
Thus, Simple Interest (SI) = $2597
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2597
= $7897
Thus, Amount to be paid = $7897 Answer
Similar Questions
(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 4 years.
(2) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.
(4) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(5) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.
(7) How much loan did Karen borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6842.5 to clear it?
(8) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?
(9) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.
(10) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.