Question:
Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 4 years.
Correct Answer
$5056
Solution And Explanation
Solution
Given,
Principal (P) = $3950
Rate of Simple Interest (SI) = 7%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $3950 × 7% × 4
= $3950 ×7/100 × 4
= 3950 × 7 × 4/100
= 27650 × 4/100
= 110600/100
= $1106
Thus, Simple Interest = $1106
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 = $3950 + $1106
= $5056
Thus, Amount to be paid = $5056 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 = $3950
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 4 years
Thus, Amount (A)
= $3950 + ($3950 × 7% × 4)
= $3950 + ($3950 ×7/100 × 4)
= $3950 + (3950 × 7 × 4/100)
= $3950 + (27650 × 4/100)
= $3950 + (110600/100)
= $3950 + $1106 = $5056
Thus, Amount (A) to be paid = $5056 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3950, the simple interest in 1 year
= 7/100 × 3950
= 7 × 3950/100
= 27650/100 = $276.5
Thus, simple interest for 1 year = $276.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $276.5 × 4 = $1106
Thus, Simple Interest (SI) = $1106
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3950 + $1106
= $5056
Thus, Amount to be paid = $5056 Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(3) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 3 years.
(5) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(6) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(7) If Jessica paid $4350 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?
(9) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.