Question:
Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
Correct Answer
$9291
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 7%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $5700 × 7% × 9
= $5700 ×7/100 × 9
= 5700 × 7 × 9/100
= 39900 × 9/100
= 359100/100
= $3591
Thus, Simple Interest = $3591
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 = $5700 + $3591
= $9291
Thus, Amount to be paid = $9291 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 = $5700
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5700 + ($5700 × 7% × 9)
= $5700 + ($5700 ×7/100 × 9)
= $5700 + (5700 × 7 × 9/100)
= $5700 + (39900 × 9/100)
= $5700 + (359100/100)
= $5700 + $3591 = $9291
Thus, Amount (A) to be paid = $9291 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5700, the simple interest in 1 year
= 7/100 × 5700
= 7 × 5700/100
= 39900/100 = $399
Thus, simple interest for 1 year = $399
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $399 × 9 = $3591
Thus, Simple Interest (SI) = $3591
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $3591
= $9291
Thus, Amount to be paid = $9291 Answer
Similar Questions
(1) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.
(3) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?
(4) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(5) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?
(7) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.
(8) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(9) How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?
(10) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.