Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.
Correct Answer
$6836.5
Solution And Explanation
Solution
Given,
Principal (P) = $5650
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) = $5650 × 3% × 7
= $5650 ×3/100 × 7
= 5650 × 3 × 7/100
= 16950 × 7/100
= 118650/100
= $1186.5
Thus, Simple Interest = $1186.5
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 = $5650 + $1186.5
= $6836.5
Thus, Amount to be paid = $6836.5 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 = $5650
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 7 years
Thus, Amount (A)
= $5650 + ($5650 × 3% × 7)
= $5650 + ($5650 ×3/100 × 7)
= $5650 + (5650 × 3 × 7/100)
= $5650 + (16950 × 7/100)
= $5650 + (118650/100)
= $5650 + $1186.5 = $6836.5
Thus, Amount (A) to be paid = $6836.5 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 $5650, the simple interest in 1 year
= 3/100 × 5650
= 3 × 5650/100
= 16950/100 = $169.5
Thus, simple interest for 1 year = $169.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $169.5 × 7 = $1186.5
Thus, Simple Interest (SI) = $1186.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $1186.5
= $6836.5
Thus, Amount to be paid = $6836.5 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(2) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.
(3) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(4) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?
(5) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(7) William had to pay $3920 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?
(9) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.
(10) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.