Question:
Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
Correct Answer
$4992
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 7%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 4
= $3900 ×7/100 × 4
= 3900 × 7 × 4/100
= 27300 × 4/100
= 109200/100
= $1092
Thus, Simple Interest = $1092
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 + $1092
= $4992
Thus, Amount to be paid = $4992 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) = 7%
And, Time (t) = 4 years
Thus, Amount (A)
= $3900 + ($3900 × 7% × 4)
= $3900 + ($3900 ×7/100 × 4)
= $3900 + (3900 × 7 × 4/100)
= $3900 + (27300 × 4/100)
= $3900 + (109200/100)
= $3900 + $1092 = $4992
Thus, Amount (A) to be paid = $4992 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3900, the simple interest in 1 year
= 7/100 × 3900
= 7 × 3900/100
= 27300/100 = $273
Thus, simple interest for 1 year = $273
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $273 × 4 = $1092
Thus, Simple Interest (SI) = $1092
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $1092
= $4992
Thus, Amount to be paid = $4992 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
(2) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(3) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.
(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(6) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?
(7) In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?
(8) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 4 years.