Question:
Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
Correct Answer
$7480
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 4%
Time (t) = 9 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% × 9
= $5500 ×4/100 × 9
= 5500 × 4 × 9/100
= 22000 × 9/100
= 198000/100
= $1980
Thus, Simple Interest = $1980
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 + $1980
= $7480
Thus, Amount to be paid = $7480 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) = 9 years
Thus, Amount (A)
= $5500 + ($5500 × 4% × 9)
= $5500 + ($5500 ×4/100 × 9)
= $5500 + (5500 × 4 × 9/100)
= $5500 + (22000 × 9/100)
= $5500 + (198000/100)
= $5500 + $1980 = $7480
Thus, Amount (A) to be paid = $7480 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 9 years
= Simple interest for 1 year × 9
= $220 × 9 = $1980
Thus, Simple Interest (SI) = $1980
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $1980
= $7480
Thus, Amount to be paid = $7480 Answer
Similar Questions
(1) How much loan did Sandra borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8062.5 to clear it?
(2) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.
(3) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(4) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(5) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?
(6) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 3 years.
(9) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?
(10) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?