Question:
Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.
Correct Answer
$8195
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 7%
Time (t) = 7 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) = $5500 × 7% × 7
= $5500 ×7/100 × 7
= 5500 × 7 × 7/100
= 38500 × 7/100
= 269500/100
= $2695
Thus, Simple Interest = $2695
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 + $2695
= $8195
Thus, Amount to be paid = $8195 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) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5500 + ($5500 × 7% × 7)
= $5500 + ($5500 ×7/100 × 7)
= $5500 + (5500 × 7 × 7/100)
= $5500 + (38500 × 7/100)
= $5500 + (269500/100)
= $5500 + $2695 = $8195
Thus, Amount (A) to be paid = $8195 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 $5500, the simple interest in 1 year
= 7/100 × 5500
= 7 × 5500/100
= 38500/100 = $385
Thus, simple interest for 1 year = $385
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $385 × 7 = $2695
Thus, Simple Interest (SI) = $2695
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $2695
= $8195
Thus, Amount to be paid = $8195 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 4 years.
(3) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.
(4) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(5) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.
(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.
(9) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.