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 Mary borrowed a sum of $5050 at 9% simple interest for 7 years.
(2) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(3) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(4) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
(7) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.
(8) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(9) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?
(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?