Question:
Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.
Correct Answer
$10070
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 10%
Time (t) = 9 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% × 9
= $5300 ×10/100 × 9
= 5300 × 10 × 9/100
= 53000 × 9/100
= 477000/100
= $4770
Thus, Simple Interest = $4770
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 + $4770
= $10070
Thus, Amount to be paid = $10070 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) = 9 years
Thus, Amount (A)
= $5300 + ($5300 × 10% × 9)
= $5300 + ($5300 ×10/100 × 9)
= $5300 + (5300 × 10 × 9/100)
= $5300 + (53000 × 9/100)
= $5300 + (477000/100)
= $5300 + $4770 = $10070
Thus, Amount (A) to be paid = $10070 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 9 years
= Simple interest for 1 year × 9
= $530 × 9 = $4770
Thus, Simple Interest (SI) = $4770
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $4770
= $10070
Thus, Amount to be paid = $10070 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 3 years.
(5) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(6) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 7 years.
(8) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?
(9) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.