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 Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?
(2) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.
(4) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?
(5) If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 3 years.
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.
(8) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(9) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 3 years.