Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.
Correct Answer
$9126
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 8%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 7
= $5850 ×8/100 × 7
= 5850 × 8 × 7/100
= 46800 × 7/100
= 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) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5850 + ($5850 × 8% × 7)
= $5850 + ($5850 ×8/100 × 7)
= $5850 + (5850 × 8 × 7/100)
= $5850 + (46800 × 7/100)
= $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 = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5850, the simple interest in 1 year
= 8/100 × 5850
= 8 × 5850/100
= 46800/100 = $468
Thus, simple interest for 1 year = $468
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $468 × 7 = $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) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(2) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 8 years.
(4) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(6) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.
(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.
(10) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.