Question:
Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.
Correct Answer
$9600
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 6%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 10
= $6000 ×6/100 × 10
= 6000 × 6 × 10/100
= 36000 × 10/100
= 360000/100
= $3600
Thus, Simple Interest = $3600
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 + $3600
= $9600
Thus, Amount to be paid = $9600 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) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $6000 + ($6000 × 6% × 10)
= $6000 + ($6000 ×6/100 × 10)
= $6000 + (6000 × 6 × 10/100)
= $6000 + (36000 × 10/100)
= $6000 + (360000/100)
= $6000 + $3600 = $9600
Thus, Amount (A) to be paid = $9600 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $6000, the simple interest in 1 year
= 6/100 × 6000
= 6 × 6000/100
= 36000/100 = $360
Thus, simple interest for 1 year = $360
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $360 × 10 = $3600
Thus, Simple Interest (SI) = $3600
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $3600
= $9600
Thus, Amount to be paid = $9600 Answer
Similar Questions
(1) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?
(2) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.
(3) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(4) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.
(6) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
(8) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?
(9) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.