Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.
Correct Answer
$9540
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 10%
Time (t) = 8 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% × 8
= $5300 ×10/100 × 8
= 5300 × 10 × 8/100
= 53000 × 8/100
= 424000/100
= $4240
Thus, Simple Interest = $4240
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 + $4240
= $9540
Thus, Amount to be paid = $9540 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) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 10% × 8)
= $5300 + ($5300 ×10/100 × 8)
= $5300 + (5300 × 10 × 8/100)
= $5300 + (53000 × 8/100)
= $5300 + (424000/100)
= $5300 + $4240 = $9540
Thus, Amount (A) to be paid = $9540 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 8 years
= Simple interest for 1 year × 8
= $530 × 8 = $4240
Thus, Simple Interest (SI) = $4240
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $4240
= $9540
Thus, Amount to be paid = $9540 Answer
Similar Questions
(1) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?
(3) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 3 years.
(4) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.
(5) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(7) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?
(9) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?