Question:
Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.
Correct Answer
$5460
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 10%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 4
= $3900 ×10/100 × 4
= 3900 × 10 × 4/100
= 39000 × 4/100
= 156000/100
= $1560
Thus, Simple Interest = $1560
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 + $1560
= $5460
Thus, Amount to be paid = $5460 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) = 10%
And, Time (t) = 4 years
Thus, Amount (A)
= $3900 + ($3900 × 10% × 4)
= $3900 + ($3900 ×10/100 × 4)
= $3900 + (3900 × 10 × 4/100)
= $3900 + (39000 × 4/100)
= $3900 + (156000/100)
= $3900 + $1560 = $5460
Thus, Amount (A) to be paid = $5460 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3900, the simple interest in 1 year
= 10/100 × 3900
= 10 × 3900/100
= 39000/100 = $390
Thus, simple interest for 1 year = $390
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $390 × 4 = $1560
Thus, Simple Interest (SI) = $1560
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $1560
= $5460
Thus, Amount to be paid = $5460 Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 4 years.
(2) How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?
(3) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(4) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?
(5) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?
(7) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(8) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.
(10) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.