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) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?
(2) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
(5) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.
(9) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
(10) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.