Question:
Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.
Correct Answer
$5005
Solution And Explanation
Solution
Given,
Principal (P) = $3850
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) = $3850 × 10% × 3
= $3850 ×10/100 × 3
= 3850 × 10 × 3/100
= 38500 × 3/100
= 115500/100
= $1155
Thus, Simple Interest = $1155
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 = $3850 + $1155
= $5005
Thus, Amount to be paid = $5005 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 = $3850
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 3 years
Thus, Amount (A)
= $3850 + ($3850 × 10% × 3)
= $3850 + ($3850 ×10/100 × 3)
= $3850 + (3850 × 10 × 3/100)
= $3850 + (38500 × 3/100)
= $3850 + (115500/100)
= $3850 + $1155 = $5005
Thus, Amount (A) to be paid = $5005 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 $3850, the simple interest in 1 year
= 10/100 × 3850
= 10 × 3850/100
= 38500/100 = $385
Thus, simple interest for 1 year = $385
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $385 × 3 = $1155
Thus, Simple Interest (SI) = $1155
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $1155
= $5005
Thus, Amount to be paid = $5005 Answer
Similar Questions
(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.
(2) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.
(3) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.
(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?
(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.
(7) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.
(9) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?