Question:
Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
Correct Answer
$7685
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 5%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 9
= $5300 ×5/100 × 9
= 5300 × 5 × 9/100
= 26500 × 9/100
= 238500/100
= $2385
Thus, Simple Interest = $2385
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 + $2385
= $7685
Thus, Amount to be paid = $7685 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) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5300 + ($5300 × 5% × 9)
= $5300 + ($5300 ×5/100 × 9)
= $5300 + (5300 × 5 × 9/100)
= $5300 + (26500 × 9/100)
= $5300 + (238500/100)
= $5300 + $2385 = $7685
Thus, Amount (A) to be paid = $7685 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5300, the simple interest in 1 year
= 5/100 × 5300
= 5 × 5300/100
= 26500/100 = $265
Thus, simple interest for 1 year = $265
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $265 × 9 = $2385
Thus, Simple Interest (SI) = $2385
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2385
= $7685
Thus, Amount to be paid = $7685 Answer
Similar Questions
(1) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 6% simple interest?
(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.
(3) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(4) How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?
(5) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?
(6) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.
(8) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.