Question:
What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?
Correct Answer
$5304
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 6%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 6
= $3900 ×6/100 × 6
= 3900 × 6 × 6/100
= 23400 × 6/100
= 140400/100
= $1404
Thus, Simple Interest = $1404
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 + $1404
= $5304
Thus, Amount to be paid = $5304 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) = 6%
And, Time (t) = 6 years
Thus, Amount (A)
= $3900 + ($3900 × 6% × 6)
= $3900 + ($3900 ×6/100 × 6)
= $3900 + (3900 × 6 × 6/100)
= $3900 + (23400 × 6/100)
= $3900 + (140400/100)
= $3900 + $1404 = $5304
Thus, Amount (A) to be paid = $5304 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3900, the simple interest in 1 year
= 6/100 × 3900
= 6 × 3900/100
= 23400/100 = $234
Thus, simple interest for 1 year = $234
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $234 × 6 = $1404
Thus, Simple Interest (SI) = $1404
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $1404
= $5304
Thus, Amount to be paid = $5304 Answer
Similar Questions
(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(2) How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?
(3) Elizabeth had to pay $3864 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 3 years.
(5) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(6) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(7) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?
(9) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?
(10) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.