Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 8 years.
Correct Answer
$10530
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5850 ×10/100 × 8
= 5850 × 10 × 8/100
= 58500 × 8/100
= 468000/100
= $4680
Thus, Simple Interest = $4680
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 + $4680
= $10530
Thus, Amount to be paid = $10530 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5850 + ($5850 × 10% × 8)
= $5850 + ($5850 ×10/100 × 8)
= $5850 + (5850 × 10 × 8/100)
= $5850 + (58500 × 8/100)
= $5850 + (468000/100)
= $5850 + $4680 = $10530
Thus, Amount (A) to be paid = $10530 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5850, the simple interest in 1 year
= 10/100 × 5850
= 10 × 5850/100
= 58500/100 = $585
Thus, simple interest for 1 year = $585
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $585 × 8 = $4680
Thus, Simple Interest (SI) = $4680
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $4680
= $10530
Thus, Amount to be paid = $10530 Answer
Similar Questions
(1) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(2) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(3) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 5% simple interest?
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.
(5) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(6) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 4 years.
(8) In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?
(9) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.