Question:
Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
Correct Answer
$9050
Solution And Explanation
Solution
Given,
Principal (P) = $5000
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) = $5000 × 9% × 9
= $5000 ×9/100 × 9
= 5000 × 9 × 9/100
= 45000 × 9/100
= 405000/100
= $4050
Thus, Simple Interest = $4050
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 = $5000 + $4050
= $9050
Thus, Amount to be paid = $9050 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 = $5000
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5000 + ($5000 × 9% × 9)
= $5000 + ($5000 ×9/100 × 9)
= $5000 + (5000 × 9 × 9/100)
= $5000 + (45000 × 9/100)
= $5000 + (405000/100)
= $5000 + $4050 = $9050
Thus, Amount (A) to be paid = $9050 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 $5000, the simple interest in 1 year
= 9/100 × 5000
= 9 × 5000/100
= 45000/100 = $450
Thus, simple interest for 1 year = $450
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $450 × 9 = $4050
Thus, Simple Interest (SI) = $4050
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $4050
= $9050
Thus, Amount to be paid = $9050 Answer
Similar Questions
(1) If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.
(3) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(4) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(5) Lisa had to pay $4293 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 8 years.
(7) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.
(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?
(9) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
(10) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.