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) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
(2) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.
(3) How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?
(4) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(5) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(6) How much loan did Sandra borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8062.5 to clear it?
(7) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
(8) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(9) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.