Question:
What amount does David have to pay after 5 years if he takes a loan of $3400 at 10% simple interest?
Correct Answer
$5100
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 10%
Time (t) = 5 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% × 5
= $3400 ×10/100 × 5
= 3400 × 10 × 5/100
= 34000 × 5/100
= 170000/100
= $1700
Thus, Simple Interest = $1700
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 + $1700
= $5100
Thus, Amount to be paid = $5100 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) = 5 years
Thus, Amount (A)
= $3400 + ($3400 × 10% × 5)
= $3400 + ($3400 ×10/100 × 5)
= $3400 + (3400 × 10 × 5/100)
= $3400 + (34000 × 5/100)
= $3400 + (170000/100)
= $3400 + $1700 = $5100
Thus, Amount (A) to be paid = $5100 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 5 years
= Simple interest for 1 year × 5
= $340 × 5 = $1700
Thus, Simple Interest (SI) = $1700
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $1700
= $5100
Thus, Amount to be paid = $5100 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(2) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.
(4) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 4 years.
(5) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.
(7) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(8) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?
(9) If Anthony paid $4988 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.