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) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?
(2) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 6% simple interest?
(3) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(4) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 5% simple interest?
(6) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.
(7) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(8) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.