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) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(3) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) Mary had to pay $3416 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 $3200 will amount to $3392 at a simple interest of 2% per annum?
(6) Robert had to pay $3379 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(8) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 3 years.
(10) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.