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) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.
(2) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.
(4) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?
(5) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(6) How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?
(7) Susan took a loan of $5300 at the rate of 7% 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 David borrowed a sum of $5400 at 7% simple interest for 8 years.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 4 years.
(10) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.