Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.
Correct Answer
$6669
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 2%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 7
= $5850 ×2/100 × 7
= 5850 × 2 × 7/100
= 11700 × 7/100
= 81900/100
= $819
Thus, Simple Interest = $819
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 + $819
= $6669
Thus, Amount to be paid = $6669 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) = 2%
And, Time (t) = 7 years
Thus, Amount (A)
= $5850 + ($5850 × 2% × 7)
= $5850 + ($5850 ×2/100 × 7)
= $5850 + (5850 × 2 × 7/100)
= $5850 + (11700 × 7/100)
= $5850 + (81900/100)
= $5850 + $819 = $6669
Thus, Amount (A) to be paid = $6669 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5850, the simple interest in 1 year
= 2/100 × 5850
= 2 × 5850/100
= 11700/100 = $117
Thus, simple interest for 1 year = $117
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $117 × 7 = $819
Thus, Simple Interest (SI) = $819
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $819
= $6669
Thus, Amount to be paid = $6669 Answer
Similar Questions
(1) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(2) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 7 years.
(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?
(4) 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.
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.
(6) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?
(7) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $10492 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) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(10) In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?