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) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.
(3) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(4) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(5) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?
(6) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(7) Mary had to pay $3507.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(10) What amount does John have to pay after 6 years if he takes a loan of $3200 at 4% simple interest?