Question:
What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?
Correct Answer
$5772
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 8%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 6
= $3900 ×8/100 × 6
= 3900 × 8 × 6/100
= 31200 × 6/100
= 187200/100
= $1872
Thus, Simple Interest = $1872
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 + $1872
= $5772
Thus, Amount to be paid = $5772 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) = 8%
And, Time (t) = 6 years
Thus, Amount (A)
= $3900 + ($3900 × 8% × 6)
= $3900 + ($3900 ×8/100 × 6)
= $3900 + (3900 × 8 × 6/100)
= $3900 + (31200 × 6/100)
= $3900 + (187200/100)
= $3900 + $1872 = $5772
Thus, Amount (A) to be paid = $5772 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $3900, the simple interest in 1 year
= 8/100 × 3900
= 8 × 3900/100
= 31200/100 = $312
Thus, simple interest for 1 year = $312
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $312 × 6 = $1872
Thus, Simple Interest (SI) = $1872
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $1872
= $5772
Thus, Amount to be paid = $5772 Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 8 years.
(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
(3) If Michelle paid $5544 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?
(5) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(6) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 4 years.
(8) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(9) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.