Question:
Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
Correct Answer
$9945
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 7%
Time (t) = 10 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) = $5850 × 7% × 10
= $5850 ×7/100 × 10
= 5850 × 7 × 10/100
= 40950 × 10/100
= 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) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5850 + ($5850 × 7% × 10)
= $5850 + ($5850 ×7/100 × 10)
= $5850 + (5850 × 7 × 10/100)
= $5850 + (40950 × 10/100)
= $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 = 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 $5850, the simple interest in 1 year
= 7/100 × 5850
= 7 × 5850/100
= 40950/100 = $409.5
Thus, simple interest for 1 year = $409.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $409.5 × 10 = $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) How much loan did Ashley borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7532.5 to clear it?
(2) If Paul paid $5640 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 3 years.
(4) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 4 years.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
(6) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 3 years.
(9) If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?