Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.
Correct Answer
$8716.5
Solution And Explanation
Solution
Given,
Principal (P) = $5850
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) = $5850 × 7% × 7
= $5850 ×7/100 × 7
= 5850 × 7 × 7/100
= 40950 × 7/100
= 286650/100
= $2866.5
Thus, Simple Interest = $2866.5
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 = $5850 + $2866.5
= $8716.5
Thus, Amount to be paid = $8716.5 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 = $5850
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5850 + ($5850 × 7% × 7)
= $5850 + ($5850 ×7/100 × 7)
= $5850 + (5850 × 7 × 7/100)
= $5850 + (40950 × 7/100)
= $5850 + (286650/100)
= $5850 + $2866.5 = $8716.5
Thus, Amount (A) to be paid = $8716.5 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 $5850, the simple interest in 1 year
= 7/100 × 5850
= 7 × 5850/100
= 40950/100 = $409.5
Thus, simple interest for 1 year = $409.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $409.5 × 7 = $2866.5
Thus, Simple Interest (SI) = $2866.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $2866.5
= $8716.5
Thus, Amount to be paid = $8716.5 Answer
Similar Questions
(1) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?
(2) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.
(3) If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(5) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?
(6) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(10) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?