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 10 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(2) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 8 years.
(4) If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.
(7) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 8 years.
(8) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 4 years.
(9) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 4 years.