Question:
Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.
Correct Answer
$4114
Solution And Explanation
Solution
Given,
Principal (P) = $3400
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) = $3400 × 7% × 3
= $3400 ×7/100 × 3
= 3400 × 7 × 3/100
= 23800 × 3/100
= 71400/100
= $714
Thus, Simple Interest = $714
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 = $3400 + $714
= $4114
Thus, Amount to be paid = $4114 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 = $3400
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 3 years
Thus, Amount (A)
= $3400 + ($3400 × 7% × 3)
= $3400 + ($3400 ×7/100 × 3)
= $3400 + (3400 × 7 × 3/100)
= $3400 + (23800 × 3/100)
= $3400 + (71400/100)
= $3400 + $714 = $4114
Thus, Amount (A) to be paid = $4114 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 $3400, the simple interest in 1 year
= 7/100 × 3400
= 7 × 3400/100
= 23800/100 = $238
Thus, simple interest for 1 year = $238
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $238 × 3 = $714
Thus, Simple Interest (SI) = $714
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $714
= $4114
Thus, Amount to be paid = $4114 Answer
Similar Questions
(1) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(2) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(3) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(4) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(5) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?
(6) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 7% simple interest?
(8) If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.
(10) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?