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) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.
(2) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
(3) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(4) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?
(5) 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?
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.
(7) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(8) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(9) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(10) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?