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) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?
(2) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?
(3) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(5) How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?
(6) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?
(7) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(8) How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?
(9) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.
(10) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.