Question:
Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
Correct Answer
$8555
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 5%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 9
= $5900 ×5/100 × 9
= 5900 × 5 × 9/100
= 29500 × 9/100
= 265500/100
= $2655
Thus, Simple Interest = $2655
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 + $2655
= $8555
Thus, Amount to be paid = $8555 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) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5900 + ($5900 × 5% × 9)
= $5900 + ($5900 ×5/100 × 9)
= $5900 + (5900 × 5 × 9/100)
= $5900 + (29500 × 9/100)
= $5900 + (265500/100)
= $5900 + $2655 = $8555
Thus, Amount (A) to be paid = $8555 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5900, the simple interest in 1 year
= 5/100 × 5900
= 5 × 5900/100
= 29500/100 = $295
Thus, simple interest for 1 year = $295
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $295 × 9 = $2655
Thus, Simple Interest (SI) = $2655
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $2655
= $8555
Thus, Amount to be paid = $8555 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(2) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.
(4) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(5) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
(7) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(8) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(10) How much loan did Betty borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7812.5 to clear it?