Question:
What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?
Correct Answer
$5850
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 10%
Time (t) = 5 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% × 5
= $3900 ×10/100 × 5
= 3900 × 10 × 5/100
= 39000 × 5/100
= 195000/100
= $1950
Thus, Simple Interest = $1950
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 + $1950
= $5850
Thus, Amount to be paid = $5850 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) = 5 years
Thus, Amount (A)
= $3900 + ($3900 × 10% × 5)
= $3900 + ($3900 ×10/100 × 5)
= $3900 + (3900 × 10 × 5/100)
= $3900 + (39000 × 5/100)
= $3900 + (195000/100)
= $3900 + $1950 = $5850
Thus, Amount (A) to be paid = $5850 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 5 years
= Simple interest for 1 year × 5
= $390 × 5 = $1950
Thus, Simple Interest (SI) = $1950
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $1950
= $5850
Thus, Amount to be paid = $5850 Answer
Similar Questions
(1) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 3 years.
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 3 years.
(3) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9685 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.
(7) If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 4 years.
(9) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?
(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 4% simple interest?