Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 7 years.
Correct Answer
$9010
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 10%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 7
= $5300 ×10/100 × 7
= 5300 × 10 × 7/100
= 53000 × 7/100
= 371000/100
= $3710
Thus, Simple Interest = $3710
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 + $3710
= $9010
Thus, Amount to be paid = $9010 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) = 10%
And, Time (t) = 7 years
Thus, Amount (A)
= $5300 + ($5300 × 10% × 7)
= $5300 + ($5300 ×10/100 × 7)
= $5300 + (5300 × 10 × 7/100)
= $5300 + (53000 × 7/100)
= $5300 + (371000/100)
= $5300 + $3710 = $9010
Thus, Amount (A) to be paid = $9010 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5300, the simple interest in 1 year
= 10/100 × 5300
= 10 × 5300/100
= 53000/100 = $530
Thus, simple interest for 1 year = $530
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $530 × 7 = $3710
Thus, Simple Interest (SI) = $3710
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $3710
= $9010
Thus, Amount to be paid = $9010 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.
(4) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.
(5) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(6) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?
(8) If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.
(10) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.