Question:
Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.
Correct Answer
$7700
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 5%
Time (t) = 8 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% × 8
= $5500 ×5/100 × 8
= 5500 × 5 × 8/100
= 27500 × 8/100
= 220000/100
= $2200
Thus, Simple Interest = $2200
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 + $2200
= $7700
Thus, Amount to be paid = $7700 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) = 8 years
Thus, Amount (A)
= $5500 + ($5500 × 5% × 8)
= $5500 + ($5500 ×5/100 × 8)
= $5500 + (5500 × 5 × 8/100)
= $5500 + (27500 × 8/100)
= $5500 + (220000/100)
= $5500 + $2200 = $7700
Thus, Amount (A) to be paid = $7700 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 8 years
= Simple interest for 1 year × 8
= $275 × 8 = $2200
Thus, Simple Interest (SI) = $2200
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $2200
= $7700
Thus, Amount to be paid = $7700 Answer
Similar Questions
(1) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(3) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?
(4) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(7) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(8) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(9) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?
(10) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.