Question:
Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 4 years.
Correct Answer
$4466
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 4%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 4
= $3850 ×4/100 × 4
= 3850 × 4 × 4/100
= 15400 × 4/100
= 61600/100
= $616
Thus, Simple Interest = $616
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 + $616
= $4466
Thus, Amount to be paid = $4466 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) = 4%
And, Time (t) = 4 years
Thus, Amount (A)
= $3850 + ($3850 × 4% × 4)
= $3850 + ($3850 ×4/100 × 4)
= $3850 + (3850 × 4 × 4/100)
= $3850 + (15400 × 4/100)
= $3850 + (61600/100)
= $3850 + $616 = $4466
Thus, Amount (A) to be paid = $4466 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3850, the simple interest in 1 year
= 4/100 × 3850
= 4 × 3850/100
= 15400/100 = $154
Thus, simple interest for 1 year = $154
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $154 × 4 = $616
Thus, Simple Interest (SI) = $616
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $616
= $4466
Thus, Amount to be paid = $4466 Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.
(2) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.
(3) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
(4) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(5) If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(7) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
(9) If Matthew paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.