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) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 4 years.
(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
(4) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?
(5) If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(7) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(8) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?
(10) In how much time a principal of $3200 will amount to $4000 at a simple interest of 5% per annum?