Question:
What amount does David have to pay after 5 years if he takes a loan of $3400 at 5% simple interest?
Correct Answer
$4250
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 5%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 5
= $3400 ×5/100 × 5
= 3400 × 5 × 5/100
= 17000 × 5/100
= 85000/100
= $850
Thus, Simple Interest = $850
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 + $850
= $4250
Thus, Amount to be paid = $4250 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) = 5%
And, Time (t) = 5 years
Thus, Amount (A)
= $3400 + ($3400 × 5% × 5)
= $3400 + ($3400 ×5/100 × 5)
= $3400 + (3400 × 5 × 5/100)
= $3400 + (17000 × 5/100)
= $3400 + (85000/100)
= $3400 + $850 = $4250
Thus, Amount (A) to be paid = $4250 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3400, the simple interest in 1 year
= 5/100 × 3400
= 5 × 3400/100
= 17000/100 = $170
Thus, simple interest for 1 year = $170
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $170 × 5 = $850
Thus, Simple Interest (SI) = $850
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $850
= $4250
Thus, Amount to be paid = $4250 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.
(2) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
(3) If Patricia paid $3654 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?
(5) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(7) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?
(8) William had to pay $3815 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.