Question:
Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
Correct Answer
$9617
Solution And Explanation
Solution
Given,
Principal (P) = $5900
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) = $5900 × 7% × 9
= $5900 ×7/100 × 9
= 5900 × 7 × 9/100
= 41300 × 9/100
= 371700/100
= $3717
Thus, Simple Interest = $3717
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 = $5900 + $3717
= $9617
Thus, Amount to be paid = $9617 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 = $5900
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5900 + ($5900 × 7% × 9)
= $5900 + ($5900 ×7/100 × 9)
= $5900 + (5900 × 7 × 9/100)
= $5900 + (41300 × 9/100)
= $5900 + (371700/100)
= $5900 + $3717 = $9617
Thus, Amount (A) to be paid = $9617 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 $5900, the simple interest in 1 year
= 7/100 × 5900
= 7 × 5900/100
= 41300/100 = $413
Thus, simple interest for 1 year = $413
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $413 × 9 = $3717
Thus, Simple Interest (SI) = $3717
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $3717
= $9617
Thus, Amount to be paid = $9617 Answer
Similar Questions
(1) If Robert paid $3348 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 7 years.
(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.
(5) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 3% simple interest.
(6) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(7) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?
(8) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.
(9) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 10% simple interest?
(10) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.