Question:
What amount does William have to pay after 5 years if he takes a loan of $3500 at 9% simple interest?
Correct Answer
$5075
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 9%
Time (t) = 5 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) = $3500 × 9% × 5
= $3500 ×9/100 × 5
= 3500 × 9 × 5/100
= 31500 × 5/100
= 157500/100
= $1575
Thus, Simple Interest = $1575
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 = $3500 + $1575
= $5075
Thus, Amount to be paid = $5075 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 = $3500
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 5 years
Thus, Amount (A)
= $3500 + ($3500 × 9% × 5)
= $3500 + ($3500 ×9/100 × 5)
= $3500 + (3500 × 9 × 5/100)
= $3500 + (31500 × 5/100)
= $3500 + (157500/100)
= $3500 + $1575 = $5075
Thus, Amount (A) to be paid = $5075 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 $3500, the simple interest in 1 year
= 9/100 × 3500
= 9 × 3500/100
= 31500/100 = $315
Thus, simple interest for 1 year = $315
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $315 × 5 = $1575
Thus, Simple Interest (SI) = $1575
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $1575
= $5075
Thus, Amount to be paid = $5075 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?
(2) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
(3) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?
(4) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(6) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.
(8) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(9) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(10) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.