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) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 4 years.
(2) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?
(3) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?
(4) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.
(6) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.
(8) James had to pay $3270 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Kenneth had to pay $5300 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.