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 after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 4 years.
(3) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.
(5) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(8) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.