Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.
Correct Answer
$9945
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 10%
Time (t) = 7 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% × 7
= $5850 ×10/100 × 7
= 5850 × 10 × 7/100
= 58500 × 7/100
= 409500/100
= $4095
Thus, Simple Interest = $4095
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 + $4095
= $9945
Thus, Amount to be paid = $9945 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) = 7 years
Thus, Amount (A)
= $5850 + ($5850 × 10% × 7)
= $5850 + ($5850 ×10/100 × 7)
= $5850 + (5850 × 10 × 7/100)
= $5850 + (58500 × 7/100)
= $5850 + (409500/100)
= $5850 + $4095 = $9945
Thus, Amount (A) to be paid = $9945 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 7 years
= Simple interest for 1 year × 7
= $585 × 7 = $4095
Thus, Simple Interest (SI) = $4095
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $4095
= $9945
Thus, Amount to be paid = $9945 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 10% simple interest?
(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.
(5) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?
(6) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?
(7) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 4 years.
(10) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?