Question:
Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 3 years.
Correct Answer
$3808
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 4%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 3
= $3400 ×4/100 × 3
= 3400 × 4 × 3/100
= 13600 × 3/100
= 40800/100
= $408
Thus, Simple Interest = $408
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 + $408
= $3808
Thus, Amount to be paid = $3808 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) = 4%
And, Time (t) = 3 years
Thus, Amount (A)
= $3400 + ($3400 × 4% × 3)
= $3400 + ($3400 ×4/100 × 3)
= $3400 + (3400 × 4 × 3/100)
= $3400 + (13600 × 3/100)
= $3400 + (40800/100)
= $3400 + $408 = $3808
Thus, Amount (A) to be paid = $3808 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3400, the simple interest in 1 year
= 4/100 × 3400
= 4 × 3400/100
= 13600/100 = $136
Thus, simple interest for 1 year = $136
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $136 × 3 = $408
Thus, Simple Interest (SI) = $408
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $408
= $3808
Thus, Amount to be paid = $3808 Answer
Similar Questions
(1) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?
(2) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.
(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(5) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(6) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.
(8) Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?