Question:
Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.
Correct Answer
$8100
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 5%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 7
= $6000 ×5/100 × 7
= 6000 × 5 × 7/100
= 30000 × 7/100
= 210000/100
= $2100
Thus, Simple Interest = $2100
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 + $2100
= $8100
Thus, Amount to be paid = $8100 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) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $6000 + ($6000 × 5% × 7)
= $6000 + ($6000 ×5/100 × 7)
= $6000 + (6000 × 5 × 7/100)
= $6000 + (30000 × 7/100)
= $6000 + (210000/100)
= $6000 + $2100 = $8100
Thus, Amount (A) to be paid = $8100 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $6000, the simple interest in 1 year
= 5/100 × 6000
= 5 × 6000/100
= 30000/100 = $300
Thus, simple interest for 1 year = $300
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $300 × 7 = $2100
Thus, Simple Interest (SI) = $2100
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $2100
= $8100
Thus, Amount to be paid = $8100 Answer
Similar Questions
(1) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?
(2) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?
(4) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.
(5) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?
(7) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.
(8) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?
(9) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?
(10) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.