Question:
What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?
Correct Answer
$6006
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 9%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $3900 × 9% × 6
= $3900 ×9/100 × 6
= 3900 × 9 × 6/100
= 35100 × 6/100
= 210600/100
= $2106
Thus, Simple Interest = $2106
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 = $3900 + $2106
= $6006
Thus, Amount to be paid = $6006 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 = $3900
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 6 years
Thus, Amount (A)
= $3900 + ($3900 × 9% × 6)
= $3900 + ($3900 ×9/100 × 6)
= $3900 + (3900 × 9 × 6/100)
= $3900 + (35100 × 6/100)
= $3900 + (210600/100)
= $3900 + $2106 = $6006
Thus, Amount (A) to be paid = $6006 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3900, the simple interest in 1 year
= 9/100 × 3900
= 9 × 3900/100
= 35100/100 = $351
Thus, simple interest for 1 year = $351
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $351 × 6 = $2106
Thus, Simple Interest (SI) = $2106
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $2106
= $6006
Thus, Amount to be paid = $6006 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.
(2) How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?
(3) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.
(4) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(7) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?
(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 8 years.
(10) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?