Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 7 years.
Correct Answer
$6715.5
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 3%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $5550 × 3% × 7
= $5550 ×3/100 × 7
= 5550 × 3 × 7/100
= 16650 × 7/100
= 116550/100
= $1165.5
Thus, Simple Interest = $1165.5
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 = $5550 + $1165.5
= $6715.5
Thus, Amount to be paid = $6715.5 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 = $5550
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 7 years
Thus, Amount (A)
= $5550 + ($5550 × 3% × 7)
= $5550 + ($5550 ×3/100 × 7)
= $5550 + (5550 × 3 × 7/100)
= $5550 + (16650 × 7/100)
= $5550 + (116550/100)
= $5550 + $1165.5 = $6715.5
Thus, Amount (A) to be paid = $6715.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5550, the simple interest in 1 year
= 3/100 × 5550
= 3 × 5550/100
= 16650/100 = $166.5
Thus, simple interest for 1 year = $166.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $166.5 × 7 = $1165.5
Thus, Simple Interest (SI) = $1165.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $1165.5
= $6715.5
Thus, Amount to be paid = $6715.5 Answer
Similar Questions
(1) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.
(3) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(4) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?
(5) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(6) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.
(9) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 3 years.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 7 years.