Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.
Correct Answer
$8639
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 9%
Time (t) = 7 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% × 7
= $5300 ×9/100 × 7
= 5300 × 9 × 7/100
= 47700 × 7/100
= 333900/100
= $3339
Thus, Simple Interest = $3339
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 + $3339
= $8639
Thus, Amount to be paid = $8639 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) = 7 years
Thus, Amount (A)
= $5300 + ($5300 × 9% × 7)
= $5300 + ($5300 ×9/100 × 7)
= $5300 + (5300 × 9 × 7/100)
= $5300 + (47700 × 7/100)
= $5300 + (333900/100)
= $5300 + $3339 = $8639
Thus, Amount (A) to be paid = $8639 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 7 years
= Simple interest for 1 year × 7
= $477 × 7 = $3339
Thus, Simple Interest (SI) = $3339
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $3339
= $8639
Thus, Amount to be paid = $8639 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.
(2) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?
(4) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 7% simple interest?
(5) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.
(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?
(8) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.
(10) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.