Question:
Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.
Correct Answer
$5070
Solution And Explanation
Solution
Given,
Principal (P) = $3900
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) = $3900 × 10% × 3
= $3900 ×10/100 × 3
= 3900 × 10 × 3/100
= 39000 × 3/100
= 117000/100
= $1170
Thus, Simple Interest = $1170
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 = $3900 + $1170
= $5070
Thus, Amount to be paid = $5070 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 = $3900
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 3 years
Thus, Amount (A)
= $3900 + ($3900 × 10% × 3)
= $3900 + ($3900 ×10/100 × 3)
= $3900 + (3900 × 10 × 3/100)
= $3900 + (39000 × 3/100)
= $3900 + (117000/100)
= $3900 + $1170 = $5070
Thus, Amount (A) to be paid = $5070 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 $3900, the simple interest in 1 year
= 10/100 × 3900
= 10 × 3900/100
= 39000/100 = $390
Thus, simple interest for 1 year = $390
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $390 × 3 = $1170
Thus, Simple Interest (SI) = $1170
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $1170
= $5070
Thus, Amount to be paid = $5070 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.
(5) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.
(6) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(7) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.
(9) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
(10) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.