Question:
Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.
Correct Answer
$7040
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 4%
Time (t) = 7 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% × 7
= $5500 ×4/100 × 7
= 5500 × 4 × 7/100
= 22000 × 7/100
= 154000/100
= $1540
Thus, Simple Interest = $1540
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 + $1540
= $7040
Thus, Amount to be paid = $7040 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) = 7 years
Thus, Amount (A)
= $5500 + ($5500 × 4% × 7)
= $5500 + ($5500 ×4/100 × 7)
= $5500 + (5500 × 4 × 7/100)
= $5500 + (22000 × 7/100)
= $5500 + (154000/100)
= $5500 + $1540 = $7040
Thus, Amount (A) to be paid = $7040 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 7 years
= Simple interest for 1 year × 7
= $220 × 7 = $1540
Thus, Simple Interest (SI) = $1540
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $1540
= $7040
Thus, Amount to be paid = $7040 Answer
Similar Questions
(1) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.
(2) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
(4) How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?
(5) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(7) Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 5% simple interest?
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.