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 after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
(2) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(3) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(5) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?
(6) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 4 years.
(8) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?
(9) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(10) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.