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 if Christopher borrowed a sum of $4000 at 2% simple interest for 4 years.
(2) In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?
(3) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8050 to clear it?
(4) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(5) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.
(6) How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?
(7) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?
(8) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 4 years.
(9) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.
(10) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.