Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.
Correct Answer
$7488
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 4%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 7
= $5850 ×4/100 × 7
= 5850 × 4 × 7/100
= 23400 × 7/100
= 163800/100
= $1638
Thus, Simple Interest = $1638
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 + $1638
= $7488
Thus, Amount to be paid = $7488 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) = 4%
And, Time (t) = 7 years
Thus, Amount (A)
= $5850 + ($5850 × 4% × 7)
= $5850 + ($5850 ×4/100 × 7)
= $5850 + (5850 × 4 × 7/100)
= $5850 + (23400 × 7/100)
= $5850 + (163800/100)
= $5850 + $1638 = $7488
Thus, Amount (A) to be paid = $7488 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5850, the simple interest in 1 year
= 4/100 × 5850
= 4 × 5850/100
= 23400/100 = $234
Thus, simple interest for 1 year = $234
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $234 × 7 = $1638
Thus, Simple Interest (SI) = $1638
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $1638
= $7488
Thus, Amount to be paid = $7488 Answer
Similar Questions
(1) How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?
(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(3) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 8 years.
(5) 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.
(6) What amount will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?
(7) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(10) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?