Question:
Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.
Correct Answer
$6655
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 3%
Time (t) = 7 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% × 7
= $5500 ×3/100 × 7
= 5500 × 3 × 7/100
= 16500 × 7/100
= 115500/100
= $1155
Thus, Simple Interest = $1155
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 + $1155
= $6655
Thus, Amount to be paid = $6655 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) = 7 years
Thus, Amount (A)
= $5500 + ($5500 × 3% × 7)
= $5500 + ($5500 ×3/100 × 7)
= $5500 + (5500 × 3 × 7/100)
= $5500 + (16500 × 7/100)
= $5500 + (115500/100)
= $5500 + $1155 = $6655
Thus, Amount (A) to be paid = $6655 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 7 years
= Simple interest for 1 year × 7
= $165 × 7 = $1155
Thus, Simple Interest (SI) = $1155
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $1155
= $6655
Thus, Amount to be paid = $6655 Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.
(3) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(5) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(6) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 10% simple interest?
(7) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 7% simple interest?
(9) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?
(10) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.