Question:
What amount does David have to pay after 6 years if he takes a loan of $3400 at 10% simple interest?
Correct Answer
$5440
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 10%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 6
= $3400 ×10/100 × 6
= 3400 × 10 × 6/100
= 34000 × 6/100
= 204000/100
= $2040
Thus, Simple Interest = $2040
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 + $2040
= $5440
Thus, Amount to be paid = $5440 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) = 10%
And, Time (t) = 6 years
Thus, Amount (A)
= $3400 + ($3400 × 10% × 6)
= $3400 + ($3400 ×10/100 × 6)
= $3400 + (3400 × 10 × 6/100)
= $3400 + (34000 × 6/100)
= $3400 + (204000/100)
= $3400 + $2040 = $5440
Thus, Amount (A) to be paid = $5440 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3400, the simple interest in 1 year
= 10/100 × 3400
= 10 × 3400/100
= 34000/100 = $340
Thus, simple interest for 1 year = $340
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $340 × 6 = $2040
Thus, Simple Interest (SI) = $2040
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $2040
= $5440
Thus, Amount to be paid = $5440 Answer
Similar Questions
(1) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 4% simple interest?
(2) How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?
(3) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(5) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.
(6) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(8) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(9) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?