Question:
Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
Correct Answer
$7956
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 4%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 9
= $5850 ×4/100 × 9
= 5850 × 4 × 9/100
= 23400 × 9/100
= 210600/100
= $2106
Thus, Simple Interest = $2106
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 + $2106
= $7956
Thus, Amount to be paid = $7956 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) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5850 + ($5850 × 4% × 9)
= $5850 + ($5850 ×4/100 × 9)
= $5850 + (5850 × 4 × 9/100)
= $5850 + (23400 × 9/100)
= $5850 + (210600/100)
= $5850 + $2106 = $7956
Thus, Amount (A) to be paid = $7956 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5850, the simple interest in 1 year
= 4/100 × 5850
= 4 × 5850/100
= 23400/100 = $234
Thus, simple interest for 1 year = $234
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $234 × 9 = $2106
Thus, Simple Interest (SI) = $2106
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $2106
= $7956
Thus, Amount to be paid = $7956 Answer
Similar Questions
(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.
(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 3% simple interest?
(4) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?
(5) If Barbara paid $4118 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11765 to clear the loan, then find the time period of the loan.
(7) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(8) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(9) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.