Question:
Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
Correct Answer
$7975
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 5%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5500 × 5% × 9
= $5500 ×5/100 × 9
= 5500 × 5 × 9/100
= 27500 × 9/100
= 247500/100
= $2475
Thus, Simple Interest = $2475
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 = $5500 + $2475
= $7975
Thus, Amount to be paid = $7975 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 = $5500
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5500 + ($5500 × 5% × 9)
= $5500 + ($5500 ×5/100 × 9)
= $5500 + (5500 × 5 × 9/100)
= $5500 + (27500 × 9/100)
= $5500 + (247500/100)
= $5500 + $2475 = $7975
Thus, Amount (A) to be paid = $7975 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5500, the simple interest in 1 year
= 5/100 × 5500
= 5 × 5500/100
= 27500/100 = $275
Thus, simple interest for 1 year = $275
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $275 × 9 = $2475
Thus, Simple Interest (SI) = $2475
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $2475
= $7975
Thus, Amount to be paid = $7975 Answer
Similar Questions
(1) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(2) If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.
(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?
(5) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?
(6) Nancy took a loan of $6300 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.
(7) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?
(9) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(10) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.