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) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(2) How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?
(3) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9512 to clear the loan, then find the time period of the loan.
(4) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?
(7) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.
(8) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 3 years.