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) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 8 years.
(2) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(3) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(4) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?
(5) What amount will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?
(6) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?
(9) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(10) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?