Question:
Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.
Correct Answer
$6820
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5500 ×3/100 × 8
= 5500 × 3 × 8/100
= 16500 × 8/100
= 132000/100
= $1320
Thus, Simple Interest = $1320
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 + $1320
= $6820
Thus, Amount to be paid = $6820 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5500 + ($5500 × 3% × 8)
= $5500 + ($5500 ×3/100 × 8)
= $5500 + (5500 × 3 × 8/100)
= $5500 + (16500 × 8/100)
= $5500 + (132000/100)
= $5500 + $1320 = $6820
Thus, Amount (A) to be paid = $6820 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5500, the simple interest in 1 year
= 3/100 × 5500
= 3 × 5500/100
= 16500/100 = $165
Thus, simple interest for 1 year = $165
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $165 × 8 = $1320
Thus, Simple Interest (SI) = $1320
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $1320
= $6820
Thus, Amount to be paid = $6820 Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9089 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.
(3) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(4) How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?
(5) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(6) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 3 years.
(8) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(9) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(10) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.