Question:
Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.
Correct Answer
$3706
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 3%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 3
= $3400 ×3/100 × 3
= 3400 × 3 × 3/100
= 10200 × 3/100
= 30600/100
= $306
Thus, Simple Interest = $306
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 + $306
= $3706
Thus, Amount to be paid = $3706 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) = 3%
And, Time (t) = 3 years
Thus, Amount (A)
= $3400 + ($3400 × 3% × 3)
= $3400 + ($3400 ×3/100 × 3)
= $3400 + (3400 × 3 × 3/100)
= $3400 + (10200 × 3/100)
= $3400 + (30600/100)
= $3400 + $306 = $3706
Thus, Amount (A) to be paid = $3706 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3400, the simple interest in 1 year
= 3/100 × 3400
= 3 × 3400/100
= 10200/100 = $102
Thus, simple interest for 1 year = $102
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $102 × 3 = $306
Thus, Simple Interest (SI) = $306
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $306
= $3706
Thus, Amount to be paid = $3706 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
(2) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?
(4) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(5) If Jennifer borrowed $3250 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.
(7) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?
(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(9) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.