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) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 4 years.
(2) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(3) How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?
(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.
(5) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 5% simple interest?
(6) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?
(7) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(8) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 5% simple interest?
(9) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(10) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 7 years.