Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 8 years.
Correct Answer
$9126
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 7%
Time (t) = 8 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% × 8
= $5850 ×7/100 × 8
= 5850 × 7 × 8/100
= 40950 × 8/100
= 327600/100
= $3276
Thus, Simple Interest = $3276
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 + $3276
= $9126
Thus, Amount to be paid = $9126 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) = 8 years
Thus, Amount (A)
= $5850 + ($5850 × 7% × 8)
= $5850 + ($5850 ×7/100 × 8)
= $5850 + (5850 × 7 × 8/100)
= $5850 + (40950 × 8/100)
= $5850 + (327600/100)
= $5850 + $3276 = $9126
Thus, Amount (A) to be paid = $9126 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 8 years
= Simple interest for 1 year × 8
= $409.5 × 8 = $3276
Thus, Simple Interest (SI) = $3276
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $3276
= $9126
Thus, Amount to be paid = $9126 Answer
Similar Questions
(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.
(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 4 years.
(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.
(8) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?
(9) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?