Question:
Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 3 years.
Correct Answer
$4598
Solution And Explanation
Solution
Given,
Principal (P) = $3800
Rate of Simple Interest (SI) = 7%
Time (t) = 3 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) = $3800 × 7% × 3
= $3800 ×7/100 × 3
= 3800 × 7 × 3/100
= 26600 × 3/100
= 79800/100
= $798
Thus, Simple Interest = $798
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 = $3800 + $798
= $4598
Thus, Amount to be paid = $4598 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 = $3800
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 3 years
Thus, Amount (A)
= $3800 + ($3800 × 7% × 3)
= $3800 + ($3800 ×7/100 × 3)
= $3800 + (3800 × 7 × 3/100)
= $3800 + (26600 × 3/100)
= $3800 + (79800/100)
= $3800 + $798 = $4598
Thus, Amount (A) to be paid = $4598 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 $3800, the simple interest in 1 year
= 7/100 × 3800
= 7 × 3800/100
= 26600/100 = $266
Thus, simple interest for 1 year = $266
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $266 × 3 = $798
Thus, Simple Interest (SI) = $798
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3800 + $798
= $4598
Thus, Amount to be paid = $4598 Answer
Similar Questions
(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 3 years.
(2) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.
(3) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(4) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if William borrowed a sum of $3250 at a 5% simple interest?
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 7 years.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 4 years.
(9) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.