Question:
What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
Correct Answer
$4828
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 7%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 6
= $3400 ×7/100 × 6
= 3400 × 7 × 6/100
= 23800 × 6/100
= 142800/100
= $1428
Thus, Simple Interest = $1428
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 + $1428
= $4828
Thus, Amount to be paid = $4828 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) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $3400 + ($3400 × 7% × 6)
= $3400 + ($3400 ×7/100 × 6)
= $3400 + (3400 × 7 × 6/100)
= $3400 + (23800 × 6/100)
= $3400 + (142800/100)
= $3400 + $1428 = $4828
Thus, Amount (A) to be paid = $4828 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3400, the simple interest in 1 year
= 7/100 × 3400
= 7 × 3400/100
= 23800/100 = $238
Thus, simple interest for 1 year = $238
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $238 × 6 = $1428
Thus, Simple Interest (SI) = $1428
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $1428
= $4828
Thus, Amount to be paid = $4828 Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?
(2) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.
(3) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(5) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
(7) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(8) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(10) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.