Question:
Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.
Correct Answer
$8160
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 4%
Time (t) = 9 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% × 9
= $6000 ×4/100 × 9
= 6000 × 4 × 9/100
= 24000 × 9/100
= 216000/100
= $2160
Thus, Simple Interest = $2160
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 + $2160
= $8160
Thus, Amount to be paid = $8160 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) = 9 years
Thus, Amount (A)
= $6000 + ($6000 × 4% × 9)
= $6000 + ($6000 ×4/100 × 9)
= $6000 + (6000 × 4 × 9/100)
= $6000 + (24000 × 9/100)
= $6000 + (216000/100)
= $6000 + $2160 = $8160
Thus, Amount (A) to be paid = $8160 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 9 years
= Simple interest for 1 year × 9
= $240 × 9 = $2160
Thus, Simple Interest (SI) = $2160
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $2160
= $8160
Thus, Amount to be paid = $8160 Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.
(3) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(4) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?
(6) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(7) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?
(8) Mary had to pay $3324.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.