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) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.
(3) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.
(4) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(6) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.
(7) What amount does James have to pay after 6 years if he takes a loan of $3000 at 7% simple interest?
(8) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?
(10) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.