Question:
Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.
Correct Answer
$4318
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 9%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 3
= $3400 ×9/100 × 3
= 3400 × 9 × 3/100
= 30600 × 3/100
= 91800/100
= $918
Thus, Simple Interest = $918
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 + $918
= $4318
Thus, Amount to be paid = $4318 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) = 9%
And, Time (t) = 3 years
Thus, Amount (A)
= $3400 + ($3400 × 9% × 3)
= $3400 + ($3400 ×9/100 × 3)
= $3400 + (3400 × 9 × 3/100)
= $3400 + (30600 × 3/100)
= $3400 + (91800/100)
= $3400 + $918 = $4318
Thus, Amount (A) to be paid = $4318 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3400, the simple interest in 1 year
= 9/100 × 3400
= 9 × 3400/100
= 30600/100 = $306
Thus, simple interest for 1 year = $306
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $306 × 3 = $918
Thus, Simple Interest (SI) = $918
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $918
= $4318
Thus, Amount to be paid = $4318 Answer
Similar Questions
(1) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(2) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.
(4) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(5) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?
(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?
(7) In how much time a principal of $3200 will amount to $3520 at a simple interest of 5% per annum?
(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.
(9) Thomas had to pay $4370 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.