Question:
Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
Correct Answer
$8800
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 6%
Time (t) = 10 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) = $5500 × 6% × 10
= $5500 ×6/100 × 10
= 5500 × 6 × 10/100
= 33000 × 10/100
= 330000/100
= $3300
Thus, Simple Interest = $3300
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 + $3300
= $8800
Thus, Amount to be paid = $8800 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) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5500 + ($5500 × 6% × 10)
= $5500 + ($5500 ×6/100 × 10)
= $5500 + (5500 × 6 × 10/100)
= $5500 + (33000 × 10/100)
= $5500 + (330000/100)
= $5500 + $3300 = $8800
Thus, Amount (A) to be paid = $8800 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 $5500, the simple interest in 1 year
= 6/100 × 5500
= 6 × 5500/100
= 33000/100 = $330
Thus, simple interest for 1 year = $330
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $330 × 10 = $3300
Thus, Simple Interest (SI) = $3300
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $3300
= $8800
Thus, Amount to be paid = $8800 Answer
Similar Questions
(1) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?
(2) In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?
(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?
(4) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(5) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.
(6) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?
(8) If Paul paid $5640 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.