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) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.
(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?
(3) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?
(4) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.
(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 2% simple interest?
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.
(7) If John paid $3456 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.