Question:
Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.
Correct Answer
$4480
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 7%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $3500 × 7% × 4
= $3500 ×7/100 × 4
= 3500 × 7 × 4/100
= 24500 × 4/100
= 98000/100
= $980
Thus, Simple Interest = $980
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 = $3500 + $980
= $4480
Thus, Amount to be paid = $4480 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 = $3500
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 4 years
Thus, Amount (A)
= $3500 + ($3500 × 7% × 4)
= $3500 + ($3500 ×7/100 × 4)
= $3500 + (3500 × 7 × 4/100)
= $3500 + (24500 × 4/100)
= $3500 + (98000/100)
= $3500 + $980 = $4480
Thus, Amount (A) to be paid = $4480 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3500, the simple interest in 1 year
= 7/100 × 3500
= 7 × 3500/100
= 24500/100 = $245
Thus, simple interest for 1 year = $245
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $245 × 4 = $980
Thus, Simple Interest (SI) = $980
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $980
= $4480
Thus, Amount to be paid = $4480 Answer
Similar Questions
(1) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 7 years.
(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(3) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(4) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(5) If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?
(7) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 10% simple interest?
(9) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(10) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.