Question:
Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
Correct Answer
$9412
Solution And Explanation
Solution
Given,
Principal (P) = $5200
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) = $5200 × 9% × 9
= $5200 ×9/100 × 9
= 5200 × 9 × 9/100
= 46800 × 9/100
= 421200/100
= $4212
Thus, Simple Interest = $4212
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 = $5200 + $4212
= $9412
Thus, Amount to be paid = $9412 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 = $5200
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5200 + ($5200 × 9% × 9)
= $5200 + ($5200 ×9/100 × 9)
= $5200 + (5200 × 9 × 9/100)
= $5200 + (46800 × 9/100)
= $5200 + (421200/100)
= $5200 + $4212 = $9412
Thus, Amount (A) to be paid = $9412 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 $5200, the simple interest in 1 year
= 9/100 × 5200
= 9 × 5200/100
= 46800/100 = $468
Thus, simple interest for 1 year = $468
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $468 × 9 = $4212
Thus, Simple Interest (SI) = $4212
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $4212
= $9412
Thus, Amount to be paid = $9412 Answer
Similar Questions
(1) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?
(2) Robert had to pay $3379 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?
(4) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.
(6) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.
(8) If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.
(10) Paul had to pay $5123 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.