Question:
Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
Correct Answer
$8024
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 4%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5900 × 4% × 9
= $5900 ×4/100 × 9
= 5900 × 4 × 9/100
= 23600 × 9/100
= 212400/100
= $2124
Thus, Simple Interest = $2124
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 = $5900 + $2124
= $8024
Thus, Amount to be paid = $8024 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 = $5900
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5900 + ($5900 × 4% × 9)
= $5900 + ($5900 ×4/100 × 9)
= $5900 + (5900 × 4 × 9/100)
= $5900 + (23600 × 9/100)
= $5900 + (212400/100)
= $5900 + $2124 = $8024
Thus, Amount (A) to be paid = $8024 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5900, the simple interest in 1 year
= 4/100 × 5900
= 4 × 5900/100
= 23600/100 = $236
Thus, simple interest for 1 year = $236
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $236 × 9 = $2124
Thus, Simple Interest (SI) = $2124
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $2124
= $8024
Thus, Amount to be paid = $8024 Answer
Similar Questions
(1) How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?
(2) 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.
(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?
(4) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?
(5) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?
(6) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(7) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 8 years.
(9) In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?
(10) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.