Question:
Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
Correct Answer
$9593
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 9%
Time (t) = 9 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% × 9
= $5300 ×9/100 × 9
= 5300 × 9 × 9/100
= 47700 × 9/100
= 429300/100
= $4293
Thus, Simple Interest = $4293
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 + $4293
= $9593
Thus, Amount to be paid = $9593 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) = 9 years
Thus, Amount (A)
= $5300 + ($5300 × 9% × 9)
= $5300 + ($5300 ×9/100 × 9)
= $5300 + (5300 × 9 × 9/100)
= $5300 + (47700 × 9/100)
= $5300 + (429300/100)
= $5300 + $4293 = $9593
Thus, Amount (A) to be paid = $9593 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 9 years
= Simple interest for 1 year × 9
= $477 × 9 = $4293
Thus, Simple Interest (SI) = $4293
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $4293
= $9593
Thus, Amount to be paid = $9593 Answer
Similar Questions
(1) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?
(2) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?
(3) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(4) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.
(6) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) If Jennifer paid $3900 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?
(9) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.