Question:
Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 3 years.
Correct Answer
$4550
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 10%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 3
= $3500 ×10/100 × 3
= 3500 × 10 × 3/100
= 35000 × 3/100
= 105000/100
= $1050
Thus, Simple Interest = $1050
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 + $1050
= $4550
Thus, Amount to be paid = $4550 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) = 10%
And, Time (t) = 3 years
Thus, Amount (A)
= $3500 + ($3500 × 10% × 3)
= $3500 + ($3500 ×10/100 × 3)
= $3500 + (3500 × 10 × 3/100)
= $3500 + (35000 × 3/100)
= $3500 + (105000/100)
= $3500 + $1050 = $4550
Thus, Amount (A) to be paid = $4550 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3500, the simple interest in 1 year
= 10/100 × 3500
= 10 × 3500/100
= 35000/100 = $350
Thus, simple interest for 1 year = $350
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $350 × 3 = $1050
Thus, Simple Interest (SI) = $1050
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $1050
= $4550
Thus, Amount to be paid = $4550 Answer
Similar Questions
(1) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?
(2) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.
(5) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.
(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(7) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(8) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.
(10) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.