Question:
Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
Correct Answer
$7700
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 4%
Time (t) = 10 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% × 10
= $5500 ×4/100 × 10
= 5500 × 4 × 10/100
= 22000 × 10/100
= 220000/100
= $2200
Thus, Simple Interest = $2200
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 + $2200
= $7700
Thus, Amount to be paid = $7700 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) = 10 years
Thus, Amount (A)
= $5500 + ($5500 × 4% × 10)
= $5500 + ($5500 ×4/100 × 10)
= $5500 + (5500 × 4 × 10/100)
= $5500 + (22000 × 10/100)
= $5500 + (220000/100)
= $5500 + $2200 = $7700
Thus, Amount (A) to be paid = $7700 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 10 years
= Simple interest for 1 year × 10
= $220 × 10 = $2200
Thus, Simple Interest (SI) = $2200
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $2200
= $7700
Thus, Amount to be paid = $7700 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(2) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?
(4) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(5) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(6) 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.
(7) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 7 years.
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 3 years.
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.