Question:
Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.
Correct Answer
$3815
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 3%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 3
= $3500 ×3/100 × 3
= 3500 × 3 × 3/100
= 10500 × 3/100
= 31500/100
= $315
Thus, Simple Interest = $315
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 + $315
= $3815
Thus, Amount to be paid = $3815 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) = 3%
And, Time (t) = 3 years
Thus, Amount (A)
= $3500 + ($3500 × 3% × 3)
= $3500 + ($3500 ×3/100 × 3)
= $3500 + (3500 × 3 × 3/100)
= $3500 + (10500 × 3/100)
= $3500 + (31500/100)
= $3500 + $315 = $3815
Thus, Amount (A) to be paid = $3815 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3500, the simple interest in 1 year
= 3/100 × 3500
= 3 × 3500/100
= 10500/100 = $105
Thus, simple interest for 1 year = $105
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $105 × 3 = $315
Thus, Simple Interest (SI) = $315
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $315
= $3815
Thus, Amount to be paid = $3815 Answer
Similar Questions
(1) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?
(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.
(3) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.
(5) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Christopher had to pay $4360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(8) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(9) Jennifer had to pay $3445 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?