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 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(2) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.
(3) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(4) How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?
(5) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 7 years.
(8) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 6% simple interest?
(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?
(10) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.