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) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.
(2) Emily had to pay $5320 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(5) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(6) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12670 to clear the loan, then find the time period of the loan.
(9) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
(10) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.