Question:
What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
Correct Answer
$5467
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 7%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $3850 × 7% × 6
= $3850 ×7/100 × 6
= 3850 × 7 × 6/100
= 26950 × 6/100
= 161700/100
= $1617
Thus, Simple Interest = $1617
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 = $3850 + $1617
= $5467
Thus, Amount to be paid = $5467 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 = $3850
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $3850 + ($3850 × 7% × 6)
= $3850 + ($3850 ×7/100 × 6)
= $3850 + (3850 × 7 × 6/100)
= $3850 + (26950 × 6/100)
= $3850 + (161700/100)
= $3850 + $1617 = $5467
Thus, Amount (A) to be paid = $5467 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3850, the simple interest in 1 year
= 7/100 × 3850
= 7 × 3850/100
= 26950/100 = $269.5
Thus, simple interest for 1 year = $269.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $269.5 × 6 = $1617
Thus, Simple Interest (SI) = $1617
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $1617
= $5467
Thus, Amount to be paid = $5467 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.
(2) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
(3) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(6) How much loan did Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?
(7) How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?
(8) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 3 years.
(9) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 4 years.
(10) How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?