Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.
Correct Answer
$8190
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 8
= $5850 ×5/100 × 8
= 5850 × 5 × 8/100
= 29250 × 8/100
= 234000/100
= $2340
Thus, Simple Interest = $2340
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 + $2340
= $8190
Thus, Amount to be paid = $8190 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) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5850 + ($5850 × 5% × 8)
= $5850 + ($5850 ×5/100 × 8)
= $5850 + (5850 × 5 × 8/100)
= $5850 + (29250 × 8/100)
= $5850 + (234000/100)
= $5850 + $2340 = $8190
Thus, Amount (A) to be paid = $8190 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5850, the simple interest in 1 year
= 5/100 × 5850
= 5 × 5850/100
= 29250/100 = $292.5
Thus, simple interest for 1 year = $292.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $292.5 × 8 = $2340
Thus, Simple Interest (SI) = $2340
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $2340
= $8190
Thus, Amount to be paid = $8190 Answer
Similar Questions
(1) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?
(4) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
(5) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.
(8) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?
(10) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.