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) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?
(2) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.
(4) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(5) How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?
(6) Patricia had to pay $3433.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?
(10) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.