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) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(2) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.
(4) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.
(7) If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.
(10) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.