Question:
Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.
Correct Answer
$4200
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 5%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 4
= $3500 ×5/100 × 4
= 3500 × 5 × 4/100
= 17500 × 4/100
= 70000/100
= $700
Thus, Simple Interest = $700
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 + $700
= $4200
Thus, Amount to be paid = $4200 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) = 5%
And, Time (t) = 4 years
Thus, Amount (A)
= $3500 + ($3500 × 5% × 4)
= $3500 + ($3500 ×5/100 × 4)
= $3500 + (3500 × 5 × 4/100)
= $3500 + (17500 × 4/100)
= $3500 + (70000/100)
= $3500 + $700 = $4200
Thus, Amount (A) to be paid = $4200 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3500, the simple interest in 1 year
= 5/100 × 3500
= 5 × 3500/100
= 17500/100 = $175
Thus, simple interest for 1 year = $175
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $175 × 4 = $700
Thus, Simple Interest (SI) = $700
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $700
= $4200
Thus, Amount to be paid = $4200 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.
(2) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(3) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(5) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.
(6) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
(8) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?
(9) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.