Question:
Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
Correct Answer
$7620
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 3%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 9
= $6000 ×3/100 × 9
= 6000 × 3 × 9/100
= 18000 × 9/100
= 162000/100
= $1620
Thus, Simple Interest = $1620
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 + $1620
= $7620
Thus, Amount to be paid = $7620 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) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $6000 + ($6000 × 3% × 9)
= $6000 + ($6000 ×3/100 × 9)
= $6000 + (6000 × 3 × 9/100)
= $6000 + (18000 × 9/100)
= $6000 + (162000/100)
= $6000 + $1620 = $7620
Thus, Amount (A) to be paid = $7620 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $6000, the simple interest in 1 year
= 3/100 × 6000
= 3 × 6000/100
= 18000/100 = $180
Thus, simple interest for 1 year = $180
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $180 × 9 = $1620
Thus, Simple Interest (SI) = $1620
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $1620
= $7620
Thus, Amount to be paid = $7620 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(2) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?
(3) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?
(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
(5) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?
(6) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
(7) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
(9) How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?
(10) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?