Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.
Correct Answer
$9594
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 8%
Time (t) = 8 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% × 8
= $5850 ×8/100 × 8
= 5850 × 8 × 8/100
= 46800 × 8/100
= 374400/100
= $3744
Thus, Simple Interest = $3744
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 + $3744
= $9594
Thus, Amount to be paid = $9594 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) = 8 years
Thus, Amount (A)
= $5850 + ($5850 × 8% × 8)
= $5850 + ($5850 ×8/100 × 8)
= $5850 + (5850 × 8 × 8/100)
= $5850 + (46800 × 8/100)
= $5850 + (374400/100)
= $5850 + $3744 = $9594
Thus, Amount (A) to be paid = $9594 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 8 years
= Simple interest for 1 year × 8
= $468 × 8 = $3744
Thus, Simple Interest (SI) = $3744
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $3744
= $9594
Thus, Amount to be paid = $9594 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.
(4) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 3 years.
(8) If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 7 years.
(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.