Question:
Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.
Correct Answer
$8400
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 4%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $6000 × 4% × 10
= $6000 ×4/100 × 10
= 6000 × 4 × 10/100
= 24000 × 10/100
= 240000/100
= $2400
Thus, Simple Interest = $2400
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 = $6000 + $2400
= $8400
Thus, Amount to be paid = $8400 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 = $6000
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 10 years
Thus, Amount (A)
= $6000 + ($6000 × 4% × 10)
= $6000 + ($6000 ×4/100 × 10)
= $6000 + (6000 × 4 × 10/100)
= $6000 + (24000 × 10/100)
= $6000 + (240000/100)
= $6000 + $2400 = $8400
Thus, Amount (A) to be paid = $8400 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $6000, the simple interest in 1 year
= 4/100 × 6000
= 4 × 6000/100
= 24000/100 = $240
Thus, simple interest for 1 year = $240
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $240 × 10 = $2400
Thus, Simple Interest (SI) = $2400
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $2400
= $8400
Thus, Amount to be paid = $8400 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(2) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(3) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) 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.
(6) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(7) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?
(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(10) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.