Question:
Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
Correct Answer
$7260
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 4%
Time (t) = 8 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) = $5500 × 4% × 8
= $5500 ×4/100 × 8
= 5500 × 4 × 8/100
= 22000 × 8/100
= 176000/100
= $1760
Thus, Simple Interest = $1760
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 + $1760
= $7260
Thus, Amount to be paid = $7260 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) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5500 + ($5500 × 4% × 8)
= $5500 + ($5500 ×4/100 × 8)
= $5500 + (5500 × 4 × 8/100)
= $5500 + (22000 × 8/100)
= $5500 + (176000/100)
= $5500 + $1760 = $7260
Thus, Amount (A) to be paid = $7260 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 $5500, the simple interest in 1 year
= 4/100 × 5500
= 4 × 5500/100
= 22000/100 = $220
Thus, simple interest for 1 year = $220
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $220 × 8 = $1760
Thus, Simple Interest (SI) = $1760
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $1760
= $7260
Thus, Amount to be paid = $7260 Answer
Similar Questions
(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 8 years.
(3) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.
(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?
(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.
(6) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.
(8) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(9) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 3 years.