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) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.
(3) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.
(5) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
(6) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(7) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?
(8) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?
(9) What amount does David have to pay after 5 years if he takes a loan of $3400 at 2% simple interest?
(10) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?