Question:
Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 4 years.
Correct Answer
$4774
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 6%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 4
= $3850 ×6/100 × 4
= 3850 × 6 × 4/100
= 23100 × 4/100
= 92400/100
= $924
Thus, Simple Interest = $924
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 + $924
= $4774
Thus, Amount to be paid = $4774 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) = 6%
And, Time (t) = 4 years
Thus, Amount (A)
= $3850 + ($3850 × 6% × 4)
= $3850 + ($3850 ×6/100 × 4)
= $3850 + (3850 × 6 × 4/100)
= $3850 + (23100 × 4/100)
= $3850 + (92400/100)
= $3850 + $924 = $4774
Thus, Amount (A) to be paid = $4774 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3850, the simple interest in 1 year
= 6/100 × 3850
= 6 × 3850/100
= 23100/100 = $231
Thus, simple interest for 1 year = $231
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $231 × 4 = $924
Thus, Simple Interest (SI) = $924
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $924
= $4774
Thus, Amount to be paid = $4774 Answer
Similar Questions
(1) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(2) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(3) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?
(4) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(5) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
(6) If Matthew paid $4704 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?
(9) In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 4 years.