Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.
Correct Answer
$9116
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 9%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 8
= $5300 ×9/100 × 8
= 5300 × 9 × 8/100
= 47700 × 8/100
= 381600/100
= $3816
Thus, Simple Interest = $3816
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 + $3816
= $9116
Thus, Amount to be paid = $9116 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) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 9% × 8)
= $5300 + ($5300 ×9/100 × 8)
= $5300 + (5300 × 9 × 8/100)
= $5300 + (47700 × 8/100)
= $5300 + (381600/100)
= $5300 + $3816 = $9116
Thus, Amount (A) to be paid = $9116 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5300, the simple interest in 1 year
= 9/100 × 5300
= 9 × 5300/100
= 47700/100 = $477
Thus, simple interest for 1 year = $477
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $477 × 8 = $3816
Thus, Simple Interest (SI) = $3816
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $3816
= $9116
Thus, Amount to be paid = $9116 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.
(2) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.
(3) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?
(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(5) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $11000 to clear the loan, then find the time period of the loan.
(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 2% simple interest?
(8) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?
(9) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(10) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.