Question:
Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
Correct Answer
$11115
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 10%
Time (t) = 9 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% × 9
= $5850 ×10/100 × 9
= 5850 × 10 × 9/100
= 58500 × 9/100
= 526500/100
= $5265
Thus, Simple Interest = $5265
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 + $5265
= $11115
Thus, Amount to be paid = $11115 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) = 9 years
Thus, Amount (A)
= $5850 + ($5850 × 10% × 9)
= $5850 + ($5850 ×10/100 × 9)
= $5850 + (5850 × 10 × 9/100)
= $5850 + (58500 × 9/100)
= $5850 + (526500/100)
= $5850 + $5265 = $11115
Thus, Amount (A) to be paid = $11115 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 9 years
= Simple interest for 1 year × 9
= $585 × 9 = $5265
Thus, Simple Interest (SI) = $5265
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $5265
= $11115
Thus, Amount to be paid = $11115 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(2) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?
(3) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(5) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 7 years.
(7) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(10) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.